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  • On partial geometries arising from maximal arcs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2021-01-07
    Mustafa Gezek, Vladimir D. Tonchev

    The subject of this paper are partial geometries \(pg(s,t,\alpha )\) with parameters \(s=d(d'-1), \ t=d'(d-1), \ \alpha =(d-1)(d'-1)\), \(d, d' \ge 2\). In all known examples, \(q=dd'\) is a power of 2 and the partial geometry arises from a maximal arc of degree d or \(d'\) in a projective plane of order q via a known construction due to Thas [28] and Wallis [34], with a single known exception of a

    更新日期:2021-01-08
  • Circular regular dessins
    J. Algebraic Comb. (IF 0.805) Pub Date : 2021-01-07
    Wenwen Fan

    A dessin is called circular if the boundary of each face is a circuit (a simple cycle). In this paper, we address the problem of characterizing edge-transitive graphs that have or do not have edge-transitive circular embeddings. We solve the problem for various families of special graphs, which show that the problem is interesting and difficult.

    更新日期:2021-01-08
  • On random permutations of finite groups
    J. Algebraic Comb. (IF 0.805) Pub Date : 2021-01-07
    D. Berend, S. Mamana

    Given a finite abelian group G, consider a uniformly random permutation of the set of all elements of G. Compute the difference of each pair of consecutive elements along the permutation. What is the number of occurrences of \(h\in G\setminus \{0\}\) in this sequence of differences? How do these numbers of occurrences behave for several group elements simultaneously? Can we get similar results for

    更新日期:2021-01-08
  • Schurity of association schemes whose thin residues are elementary abelian p -groups of rank 2
    J. Algebraic Comb. (IF 0.805) Pub Date : 2021-01-04
    Gang Chen, Bangteng Xu

    The schurity of association schemes has been studied in many papers. One of the major topics is to investigate the schurity of those association schemes whose thin residues are thin. A difficult case is that the thin residue is an elementary abelian p-group of rank 2. A class of these association schemes has played an important role in the study of p-schemes of order \(p^3\). In this paper, we study

    更新日期:2021-01-04
  • On resolvable Golomb rulers, symmetric configurations and progressive dinner parties
    J. Algebraic Comb. (IF 0.805) Pub Date : 2021-01-04
    Marco Buratti, Douglas R. Stinson

    We define a new type of Golomb ruler, which we term a resolvable Golomb ruler. These are Golomb rulers that satisfy an additional “resolvability” condition that allows them to generate resolvable symmetric configurations. The resulting configurations give rise to progressive dinner parties. In this paper, we investigate existence results for resolvable Golomb rulers and their application to the construction

    更新日期:2021-01-04
  • Eulerian polynomials via the Weyl algebra action
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-12-02
    Jose Agapito, Pasquale Petrullo, Domenico Senato, Maria M. Torres

    Through the action of the Weyl algebra on the geometric series, we establish a generalization of the Worpitzky identity and new recursive formulae for a family of polynomials including the classical Eulerian polynomials. We obtain an extension of the Dobiński formula for the sum of rook numbers of a Young diagram by replacing the geometric series with the exponential series. Also, by replacing the

    更新日期:2020-12-02
  • Moments of partitions and derivatives of higher order
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-25
    Shaul Zemel

    We define moments of partitions of integers, and show that they appear in higher-order derivatives of certain combinations of functions.

    更新日期:2020-11-25
  • Correction to “Faithful permutation representations of toroidal regular maps”
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-25
    Maria Elisa Fernandes, Claudio Alexandre Piedade

    The list of degrees of a faithful transitive permutation representation for the map

    更新日期:2020-11-25
  • Counting the decimation classes of binary vectors with relatively prime length and density
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-24
    Jonathan S. Turner, Dursun A. Bulutoglu, Daniel Baczkowski, Andrew J. Geyer

    We present a method for determining the number of decimation classes of density \(\delta \) binary vectors indexed by a finite abelian group G of size \(\ell \) and exponent \({\ell ^*}\) such that \(\delta \) is relatively prime to \({\ell ^*}\). This method is the first which is not based on exhaustive vector generation and exploits the subgroup lattice of \({{\mathbb {Z}}_{{\ell ^*}}^{\times }}\)

    更新日期:2020-11-25
  • p -almost Hadamard matrices and $$\lambda $$ λ -planes
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-24
    Manil T. Mohan

    In this work, we consider the p-almost Hadamard matrices and discuss about its connection with the orthogonal matrices corresponding to the finite projective planes, biplanes, triplanes, \(\lambda \)-planes, etc. Using multivariate analysis techniques, we obtain sufficient conditions for which such matrices are local optima to an optimization problem involving orthogonal matrix as constraints. Moreover

    更新日期:2020-11-25
  • On difference sets with small $$\lambda $$ λ
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-21
    Daniel M. Gordon

    In a 1989 paper, Arasu (Arch Math 53:622–624, 1989) used an observation about multipliers to show that no (352, 27, 2) difference set exists in any abelian group. The proof is quite short and required no computer assistance. We show that it may be applied to a wide range of parameters \((v,k,\lambda )\), particularly for small values of \(\lambda \). With it, a computer search was able to show that

    更新日期:2020-11-22
  • On pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-20
    Paul Barry, Nikolaos Pantelidis

    The group of almost Riordan arrays contains the group of Riordan arrays as a subgroup. In this note, we exhibit examples of pseudo-involutions, conditions under which we define an involution, and methods of constructing quasi-involutions in the group of almost Riordan arrays.

    更新日期:2020-11-21
  • Eigenvalues of zero-divisor graphs of finite commutative rings
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-17
    Katja Mönius

    We investigate eigenvalues of the zero-divisor graph \(\Gamma (R)\) of finite commutative rings R and study the interplay between these eigenvalues, the ring-theoretic properties of R and the graph-theoretic properties of \(\Gamma (R)\). The graph \(\Gamma (R)\) is defined as the graph with vertex set consisting of all nonzero zero-divisors of R and adjacent vertices x, y whenever \(xy = 0\). We provide

    更新日期:2020-11-17
  • Addition–deletion results for the minimal degree of logarithmic derivations of hyperplane arrangements and maximal Tjurina line arrangements
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-16
    Takuro Abe, Alexandru Dimca, Gabriel Sticlaru

    We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of \(d=9\) lines with \(n_3=6\) triple points in addition

    更新日期:2020-11-16
  • Real and complex supersolvable line arrangements in the projective plane
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-12
    Krishna Hanumanthu, Brian Harbourne

    If we regard a set of s lines in \({\mathbb P}^2\) over either the reals or the complex numbers as an algebraic plane curve, then it is an open problem to classify for all s those for which the number \(t_2\) of points of multiplicity 2 satisfies \(t_2<\lfloor s/2\rfloor \). By the Sylvester–Gallai theorem, there are no nontrivial (i.e., not a pencil or a near pencil) real arrangements with \(t_2=0\)

    更新日期:2020-11-13
  • On those multiplicative subgroups of $${\mathbb F}_{2^n}^*$$ F 2 n ∗ which are Sidon sets and/or sum-free sets
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-10
    Claude Carlet, Sihem Mesnager

    We study those multiplicative subgroups of \({\mathbb F}_{2^n}^*\) which are Sidon sets and/or sum-free sets in the group \(({\mathbb F}_{2^n},+)\). These Sidon and sum-free sets play an important role relative to the exponents of APN power functions, as shown by a paper co-authored by the first author.

    更新日期:2020-11-12
  • Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-11-03
    Antoine Douai

    Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts (weighted) lattice points in polytopes. We deduce an effective algorithm in order to compute the Ehrhart polynomial of a simplex containing the origin as an interior point.

    更新日期:2020-11-04
  • Difference equations arising from cluster algebras
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-10-24
    Yuma Mizuno

    We characterize Y/T-system-type difference equations arising from cluster algebras by triples of matrices, which we call T-data, that have a certain symplectic property. We show that all mutation loops are essentially obtained from T-data, which generalizes the general solution for period 1 quivers given by Fordy and Marsh. We also show that any T-datum associated with a periodic Y/T-system has the

    更新日期:2020-10-26
  • Optimization over Young diagrams
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-10-20
    Shmuel Onn

    We consider the problem of finding a Young diagram minimizing the sum of evaluations of a given pair of functions on the parts of the associated pair of conjugate partitions. While there are exponentially many diagrams, we show it is polynomial time solvable.

    更新日期:2020-10-20
  • Disjoint weighing matrices
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-10-19
    Hadi Kharaghani, Sho Suda, Behruz Tayfeh-Rezaie

    The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search leads to some infinite classes of disjoint weighing matrices, which in turn are shown to form commutative association schemes with 3 or 4 classes.

    更新日期:2020-10-19
  • Lattice of dominant weights of affine Kac–Moody algebras
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-10-06
    Krishanu Roy

    The dual space of the Cartan subalgebra in a Kac–Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac–Moody algebras. We give a more explicit description of the covering relations

    更新日期:2020-10-06
  • On $$A_1^2$$ A 1 2 restrictions of Weyl arrangements
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-18
    Takuro Abe, Hiroaki Terao, Tan Nhat Tran

    Let \(\mathcal {A}\) be a Weyl arrangement in an \(\ell \)-dimensional Euclidean space. The freeness of restrictions of \(\mathcal {A}\) was first settled by a case-by-case method by Orlik and Terao (Tôhoku Math J 52: 369–383, 1993), and later by a uniform argument by Douglass (Represent Theory 3: 444–456, 1999). Prior to this, Orlik and Solomon (Proc Symp Pure Math Amer Math Soc 40(2): 269–292, 1983)

    更新日期:2020-09-20
  • Inverse monoids of partial graph automorphisms
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-15
    Robert Jajcay, Tatiana Jajcayová, Nóra Szakács, Mária B. Szendrei

    A partial automorphism of a finite graph is an isomorphism between its vertex-induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the algebraic structure of such inverse monoids by the means of standard tools of inverse semigroup theory, namely Green’s relations and some properties of the natural partial

    更新日期:2020-09-15
  • Vertex-minimal planar graphs with cyclic 2-group symmetry
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-14
    Kassie Archer, Rebecca Darby, L.-K. Lauderdale, Asa Linson, Mariah K. Maxfield, Charles Schmidt, Phung T. Tran

    For the positive integer m, let \({\mathbb {Z}}_m\) denote the cyclic group of order m. Vertex-minimal planar graphs with prescribed automorphism group \({\mathbb {Z}}_m\) were first considered by Marušič. In particular, when m is odd he produced a vertex-minimal planar graph with \({\mathbb {Z}}_m\)-symmetry. Marušič then conjectured the order of a vertex-minimal planar graph with \({\mathbb {Z}}_m\)-symmetry

    更新日期:2020-09-15
  • Free field approach to the Macdonald process
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-13
    Shinji Koshida

    The Macdonald process is a stochastic process on the collection of partitions that is a (q, t)-deformed generalization of the Schur process. In this paper, we approach the Macdonald process identifying the space of symmetric functions with a Fock representation of a Heisenberg algebra. By using the free field realization of operators diagonalized by the Macdonald symmetric functions, we propose a method

    更新日期:2020-09-13
  • Tensor square of the basic spin representations of Schur covering groups for the symmetric groups
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-13
    Kazuya Aokage

    We consider the tensor square of the basic spin representations of Schur covering groups \(\widetilde{S_n}\) and \(\widetilde{S_n^{'}}\) for the symmetric group \(S_n\). It is known from work of Stembridge that the irreducible components of the tensor square of the basic spin representations for \(\widetilde{S_n}\), for n odd, are multiplicity-free and indexed by hook partitions ([3], pp. 133). In

    更新日期:2020-09-13
  • A group representation approach to balance of gain graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-13
    Matteo Cavaleri, Daniele D’Angeli, Alfredo Donno

    We study the balance of G-gain graphs, where G is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching equivalence and balance of gain graphs in terms of their adjacency matrices in \(M_n(\mathbb C G)\). Then we introduce a represented adjacency matrix, associated with a gain graph and a group representation, by extending the theory

    更新日期:2020-09-13
  • Lambda number of the power graph of a finite group
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-12
    Xuanlong Ma, Min Feng, Kaishun Wang

    The power graph \(\Gamma _G\) of a finite group G is the graph with the vertex set G, where two distinct elements are adjacent if and only if one is a power of the other. An L(2, 1)-labeling of a graph \(\Gamma \) is an assignment of labels from nonnegative integers to all vertices of \(\Gamma \) such that vertices at distance two get different labels and adjacent vertices get labels that are at least

    更新日期:2020-09-13
  • Galois connections for phylogenetic networks and their polytopes
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-12
    Stefan Forcey, Drew Scalzo

    We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labeled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with metric properties or associated with vectors. Famous examples are the Billera–Holmes–Vogtmann metric space of phylogenetic trees, and the Balanced Minimal Evolution

    更新日期:2020-09-12
  • Vertex-minimal graphs with nonabelian $${\mathbf{2}}$$ 2 -group symmetry
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-12
    L.-K. Lauderdale, Jay Zimmerman

    A graph whose full automorphism group is isomorphic to a finite group G is called a G-graph, and we let \(\alpha (G)\) denote the minimal number of vertices among all G-graphs. The value of \(\alpha (G)\) has been established for numerous infinite families of groups. In this article, we expand upon the subject matter of vertex-minimal G-graphs by computing the value of \(\alpha (G)\) when G is isomorphic

    更新日期:2020-09-12
  • Elliptic classes, McKay correspondence and theta identities
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-08
    Małgorzata Mikosz, Andrzej Weber

    We revisit the construction of elliptic class given by Borisov and Libgober for singular algebraic varieties. Assuming torus action we adjust the theory to the equivariant local situation. We study theta function identities having a geometric origin. In the case of quotient singularities \({\mathbb {C}}^n/G\), where G is a finite group the theta identities arise from McKay correspondence. The symplectic

    更新日期:2020-09-08
  • On $$\gamma $$ γ - and local $$\gamma $$ γ -vectors of the interval subdivision
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-08
    Imran Anwar, Shaheen Nazir

    We show that the \(\gamma \)-vector of the interval subdivision of a simplicial complex with a nonnegative and symmetric h-vector is nonnegative. In particular, we prove that such \(\gamma \)-vector is the f-vector of some balanced simplicial complex. Moreover, we show that the local \(\gamma \)-vector of the interval subdivision of a simplex is nonnegative; answering a question by Juhnke-Kubitzke

    更新日期:2020-09-08
  • Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-07
    Yi Zhang, Xing Gao, Yanfeng Luo

    The concept of weighted infinitesimal unitary bialgebra is an algebraic meaning of the nonhomogenous associative Yang–Baxter equation. In this paper, we equip the space of decorated planar rooted forests with a coproduct which makes it a weighted infinitesimal unitary bialgebra. Further, we construct an infinitesimal unitary Hopf algebra on decorated planar rooted forests in the sense of Loday and

    更新日期:2020-09-08
  • Sectional genus and the volume of a lattice polytope
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-07
    Ryo Kawaguchi

    For a convex lattice polytope having at least one interior lattice point, a lower bound for its volume is derived from Hibi’s lower bound theorem for the \(h^{*}\)-vector. On the other hand, it is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound for the genus of a projective curve. In this paper, we prove the equivalence of these

    更新日期:2020-09-08
  • Cohen–Macaulayness of two classes of circulant graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-07
    D. T. Hoang, H. R. Maimani, A. Mousivand, M. R. Pournaki

    Let n be a positive integer and let \(S_n\) be the set of all nonnegative integers less than n which are relatively prime to n. In this paper, we discuss structural properties of circulant graphs generated by the \(S_n's\) and their complements. In particular, we characterize when these graphs are well-covered, Cohen–Macaulay, Buchsbaum or Gorenstein.

    更新日期:2020-09-08
  • On toric ideals arising from signed graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-07
    JiSun Huh, Sangwook Kim, Boram Park

    A signed graph is a pair \((G,\tau )\) of a graph G and its sign \(\tau \), where a sign \(\tau \) is a function from \(\{ (e,v)\mid e\in E(G),v\in V(G), v\in e\}\) to \(\{1,-1\}\). Note that graphs or digraphs are special cases of signed graphs. In this paper, we study the toric ideal \(I_{(G,\tau )}\) associated with a signed graph \((G,\tau )\), and the results of the paper give a unified idea to

    更新日期:2020-09-08
  • On the critical difference of almost bipartite graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-04
    Vadim E. Levit, Eugen Mandrescu

    A set \(S\subseteq V\) is independent in a graph \(G=\left( V,E\right) \) if no two vertices from S are adjacent. The independence number \(\alpha (G)\) is the cardinality of a maximum independent set, while \(\mu (G)\) is the size of a maximum matching in G. If \(\alpha (G)+\mu (G)\) equals the order of G, then G is called a König–Egerváry graph (Deming in Discrete Math 27:23–33, 1979; Sterboul in

    更新日期:2020-09-05
  • Bisymplectic Grassmannians of planes
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-02
    Vladimiro Benedetti

    The bisymplectic Grassmannian \({{\,\mathrm{I_2Gr}\,}}(k,V)\) parametrizes k-dimensional subspaces of a vector space V which are isotropic with respect to two general skew-symmetric forms; it is a Fano projective variety which admits an action of a torus with a finite number of fixed points. In this work, we study its equivariant cohomology with complex coefficients when \(k=2\); the central result

    更新日期:2020-09-03
  • Binomial edge ideals and bounds for their regularity
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-30
    Arvind kumar

    Let G be a simple graph on n vertices and \(J_G\) denote the corresponding binomial edge ideal in \(S = K[x_1, \ldots , x_n, y_1, \ldots , y_n].\) We prove that the Castelnuovo–Mumford regularity of \(J_G\) is bounded above by \(c(G)+1\), when G is a quasi-block graph or semi-block graph. We give another proof of Saeedi Madani–Kiani regularity upper bound conjecture for chordal graphs. We obtain the

    更新日期:2020-08-30
  • On maximum additive Hermitian rank-metric codes
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-29
    Rocco Trombetti, Ferdinando Zullo

    Inspired by the work of Zhou (Des Codes Cryptogr 88:841–850, 2020) based on the paper of Schmidt (J Algebraic Combin 42(2):635–670, 2015), we investigate the equivalence issue of maximum d-codes of Hermitian matrices. More precisely, in the space \({{H}}_n(q^2)\) of Hermitian matrices over \({\mathbb {F}}_{q^2}\) we have two possible equivalences: the classical one coming from the maps that preserve

    更新日期:2020-08-29
  • Absolute points of correlations of $$PG(3,q^n)$$ P G ( 3 , q n )
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-28
    Giorgio Donati, Nicola Durante

    The sets of the absolute points of (possibly degenerate) polarities of a projective space are well known. The sets of the absolute points of (possibly degenerate) correlations, different from polarities, of \({{\mathrm{PG}}}(2,q^n)\), have been completely determined by B.C. Kestenband in 11 papers from 1990 to 2014, for non-degenerate correlations and by D’haeseleer and Durante (Electron J Combin 27(2):2–32

    更新日期:2020-08-29
  • Quasi-orthogonal cocycles, optimal sequences and a conjecture of Littlewood
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-19
    J. A. Armario, D. L. Flannery

    A quasi-orthogonal cocycle, defined over a group of order congruent to 2 modulo 4, is naturally analogous to an orthogonal cocycle (i.e., one defined over a group of order divisible by 4, and whose display matrix is Hadamard). Here we extend the theory of quasi-orthogonal cocycles in new directions, using equivalences with various optimal binary and quaternary sequences.

    更新日期:2020-08-20
  • Semisymmetric prime-valent graphs of order $$2p^3$$ 2 p 3
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-18
    Li Wang, Song-Tao Guo

    A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime and \(\Gamma \) a semisymmetric prime-valent graph of order \(2p^3\). Then, \(\Gamma \) is bipartite. Denote by \(\mathrm{Aut}(\Gamma )\) the full automorphism group of \(\Gamma \). In Du and Wang (J Algebraic Combin 41:275–302, 2015), Wang and Du (Eur J Combin 36:393–405

    更新日期:2020-08-18
  • The enumeration of spanning tree of weighted graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-17
    Jiang Zhou, Changjiang Bu

    A polynomial associated with G is defined as \(t(G,w)=\sum _{T\in {\mathbb {T}}(G)}\prod _{e\in E(T)}w_e(G)\) (\({\mathbb {T}}(G)\) is the set of spanning trees of G), which is a weighted enumeration of spanning trees of graphs. It is known that any graph G is an intersection graph of a linear hypergraph, which corresponds to a clique partition of G. In this paper, we introduce the Schur complement

    更新日期:2020-08-18
  • A combinatorial proof of the log-convexity of sequences in Riordan arrays
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-14
    Xi Chen, Yuzhenni Wang, Sai-Nan Zheng

    A Riordan array \(R=[r_{n,k}]_{n,k\ge 0}\) can be characterized by two sequences \(A=(a_n)_{n\ge 0}\) and \(Z=(z_n)_{n\ge 0}\) such that \(r_{0,0}=1, r_{0,k}=0~(k\ge 1)\) and $$\begin{aligned} r_{n+1,0}=\sum _{j\ge 0} z_j r_{n,j}, \quad r_{n+1,k+1}=\sum _{j\ge 0} a_j r_{n,k+j} \end{aligned}$$ for \(n,k\ge 0\). Using an algebraic approach, Chen, Liang and Wang showed that the sequence \((r_{n,0})_{n\ge

    更新日期:2020-08-14
  • Counting shellings of complete bipartite graphs and trees
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-08-09
    Yibo Gao, Junyao Peng

    A shelling of a graph, viewed as an abstract simplicial complex that is pure of dimension 1, is an ordering of its edges such that every edge is adjacent to some other edges appeared previously. In this paper, we focus on complete bipartite graphs and trees. For complete bipartite graphs, we obtain an exact formula for their shelling numbers. And for trees, we relate their shelling numbers to linear

    更新日期:2020-08-09
  • Unimodular polynomial matrices over finite fields
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-07-27
    Akansha Arora, Samrith Ram, Ayineedi Venkateswarlu

    We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory, we give a proof of a result of Lieb, Jordan and Helmke on the number of linear unimodular matrix polynomials over a finite field. As an application of our results, we give a new proof of a theorem of Chen and Tseng which answers a question of Niederreiter on splitting subspaces. We use

    更新日期:2020-07-27
  • Integral and distance integral Cayley graphs over generalized dihedral groups
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-22
    Jing Huang, Shuchao Li

    A graph is said to be integral (resp. distance integral) if all the eigenvalues of its adjacency matrix (resp. distance matrix) are integers. Let H be a finite abelian group, and let \({\mathscr {H}}=\langle H,b\,|\,b^2=1,bhb=h^{-1},h\in H\rangle \) be the generalized dihedral group of H. The contribution of this paper is threefold. Firstly, based on the representation theory of finite groups, we obtain

    更新日期:2020-06-22
  • Algebraic properties of Riordan subgroups
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-15
    Paul Barry, Aoife Hennessy, Nikolaos Pantelidis

    We present properties of the group structure of Riordan arrays. We examine similar properties among known Riordan subgroups, and from this, we define H[r, s, p], a family of Riordan arrays. We generalize conditions for involutions, and pseudo-involutions of H[r, s, p], and we present stabilizers of this family. We find abelian subgroups as intersections of Riordan subgroups and show some alternative

    更新日期:2020-06-15
  • Symmetric cubic graphs via rigid cells
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-13
    Marston D. E. Conder, Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič

    Properties of symmetric cubic graphs are described via their rigid cells, which are maximal connected subgraphs fixed pointwise by some involutory automorphism of the graph. This paper completes the description of rigid cells and the corresponding involutions for each of the 17 ‘action types’ of symmetric cubic graphs.

    更新日期:2020-06-13
  • Additivity of affine designs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-13
    Andrea Caggegi, Giovanni Falcone, Marco Pavone

    We show that any affine block design \(\mathcal{D}=(\mathcal{P},\mathcal{B})\) is a subset of a suitable commutative group \({\mathfrak {G}}_\mathcal{D},\) with the property that a k-subset of \(\mathcal{P}\) is a block of \(\mathcal{D}\) if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design \(\mathcal{D}\) is the group of automorphisms of \({\mathfrak

    更新日期:2020-06-13
  • Oriented matroid structures from realized root systems
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-13
    Matthew Dyer, Weijia Wang

    This paper investigates the question of uniqueness of the reduced oriented matroid structure arising from root systems of a Coxeter system in real vector spaces. We settle the question for finite Coxeter systems, irreducible affine Weyl groups and all rank three Coxeter systems. In these cases, the oriented matroid structure is unique unless W is of type \({\widetilde{A}}_n, n\ge 3\), in which case

    更新日期:2020-06-13
  • A homotopy category for graphs
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-13
    Tien Chih, Laura Scull

    We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call ‘spider moves.’ We then create a category by modding out by the 2-cells of our 2-category and use the spider moves to show that for finite graphs, this category is a homotopy category in the sense that it

    更新日期:2020-06-13
  • Representation stability of the cohomology of Springer varieties and some combinatorial consequences
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-12
    Aba Mbirika, Julianna Tymoczko

    A sequence of \(S_n\)-representations \(\{V_n\}\) is said to be uniformly representation stable if the decomposition of \(V_n = \bigoplus _{\mu } c_{\mu ,n} V(\mu )_n\) into irreducible representations is independent of n for each \(\mu \)—that is, the multiplicities \(c_{\mu ,n}\) are eventually independent of n for each \(\mu \). Church–Ellenberg–Farb proved that the cohomology of flag varieties

    更新日期:2020-06-12
  • Linear relations on LLT polynomials and their k-Schur positivity for $$k=2$$k=2
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-10
    Seung Jin Lee

    LLT polynomials are q-analogs of products of Schur functions that are known to be Schur positive by Grojnowski and Haiman. However, there is no known combinatorial formula for the coefficients in the Schur expansion. Finding such a formula also provides Schur positivity of Macdonald polynomials. On the other hand, Haiman and Haglund conjectured that LLT polynomials for skew partitions lying on k adjacent

    更新日期:2020-06-10
  • Geometric regularity of powers of two-dimensional squarefree monomial ideals
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-10
    Dancheng Lu

    Let I be a two-dimensional squarefree monomial ideal of a polynomial ring S. We evaluate the geometric regularity, \(a_i\)-invariants of \(S/I^n\) for \(i\ge 2\). It turns out that they are all linear functions in n from \(n=2\). Also, it is shown that \(\text{ g-reg }(S/I^n)={\text {reg}}(S/I^{(n)})\) for all \(n\ge 1\).

    更新日期:2020-06-10
  • An analogue of chromatic bases and p -positivity of skew Schur Q -functions
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-06-09
    Soojin Cho, JiSun Huh, Sun-Young Nam

    We investigate chromatic symmetric functions in relation to the algebra \(\varGamma \) of symmetric functions generated by Schur Q-functions. We construct natural bases of \(\varGamma \) in terms of chromatic symmetric functions. We also consider the p-positivity of skew Schur Q-functions and find a class of p-positive ribbon Schur Q-functions, making a conjecture that they are only p-positive Schur

    更新日期:2020-06-09
  • Tropical curves of hyperelliptic type
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-05-25
    Daniel Corey

    We introduce the notion of tropical curves of hyperelliptic type. These are tropical curves whose Jacobian is isomorphic to that of a hyperelliptic tropical curve, as polarized tropical abelian varieties. We show that this property depends only on the underlying graph of a tropical curve and is preserved when passing to genus \(\ge 2\) connected minors. The main result is an forbidden minors characterization

    更新日期:2020-05-25
  • Quantum walks on embeddings
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-23
    Hanmeng Zhan

    We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix U and the vertex-face incidence structure. Using the incidence graph, we derive a formula for the principal logarithm of \(U^2\), and find conditions for its underlying digraph to be an oriented graph. In particular,

    更新日期:2020-04-23
  • A classification of tetravalent non-normal Cayley graphs of order twice a prime square
    J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-20
    Li Cui, Jin-Xin Zhou, Mohsen Ghasemi, Ali Asghar Talebi, Rezvan Varmazyar

    A Cayley graph \(\mathrm{Cay}(G, S)\) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of \(\mathrm{Cay}(G, S)\). In this paper, a complete classification is given of tetravalent non-normal Cayley graphs of order \(2p^2\) for each prime p.

    更新日期:2020-04-20
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