• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-09-02

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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 • 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
• 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
• 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
• 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-18
C. J. Jones, L.-K. Lauderdale, Sarah E. Lubow, Carlie J. Triplitt

For a positive integer m, let $${\mathbb {Z}}_m$$ denote the cyclic group of order m. In this article, we discuss the orders of vertex-minimal planar graphs with prescribed automorphism group $${\mathbb {Z}}_m$$. Previously, Marušič investigated the case when m is odd, and Archer et al. considered the case when m is a power of 2. When m even and not a power of 2, Marušič conjectured the order of a

更新日期：2020-04-18
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-15
Jung-Chao Ban, Chih-Hung Chang, Yu-Hsiung Huang

Let $$G=\left\langle S|R_{A}\right\rangle$$ be a semigroup with generating set S and equivalences $$R_{A}$$ among S determined by a matrix A. This paper investigates the complexity of G-shift spaces by yielding the Petersen–Salama entropies [defined in Petersen and Salama (Theoret Comput Sci 743:64–71, 2018)]. After revealing the existence of Petersen–Salama entropy of G-shift of finite type (G-SFT)

更新日期：2020-04-15
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-13
Omar Tout

We generalize the concept of partial permutations of Ivanov and Kerov and introduce k-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product $${\mathcal {S}}_k\wr {\mathcal {S}}_n$$ algebra are polynomials in n with nonnegative integer coefficients. We use a universal algebra $${\mathcal {I}}_\infty ^k$$, which projects on the center $$Z({\mathbb 更新日期：2020-04-13 • J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-10 Ralph Morrison Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice points collinear. We prove that hyperelliptic graphs can only arise from such polygons. Along the way, we will prove certain graphs do not embed tropically in the plane 更新日期：2020-04-10 • J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-09 Michal Sedlák, Alessandro Bisio Based on the work of Vershik (J Sov Math 59(5):1029–1040, 1992), we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization problem in the field of quantum information processing. 更新日期：2020-04-09 • J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-06 Yunnan Li, Li Guo This paper studies the braidings of several Hopf algebras of rooted trees which have found broad applications. First by studying free braided dendriform algebras, we obtain the braiding of the Loday–Ronco Hopf algebra of planar binary rooted trees. We also give a variation of the braiding obtained by Foissy for the noncommutative Connes–Kreimer (a.k.a the Foissy–Holtkamp) Hopf algebra of planar rooted 更新日期：2020-04-06 • J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-06 Per Alexandersson We conjecture an explicit positive combinatorial formula for the expansion of unicellular LLT polynomials in the elementary symmetric basis. This is an analogue of the Shareshian–Wachs conjecture previously studied by Panova and the author in 2018. We show that the conjecture for unicellular LLT polynomials implies a similar formula for vertical-strip LLT polynomials. We prove positivity in the elementary 更新日期：2020-04-06 • J. Algebraic Comb. (IF 0.805) Pub Date : 2020-04-06 Paul-Henry Leemann, Mikael de la Salle We show that every finitely generated group G with an element of order at least \(\bigl (5{{\,\mathrm{rank}\,}}(G)\bigr )^{12}$$ admits a locally finite directed Cayley graph with automorphism group equal to G. If moreover G is not generalized dihedral, then the above Cayley directed graph does not have bigons. On the other hand, if G is neither generalized dicyclic nor abelian and has an element of

更新日期：2020-04-06
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-03-31
Tushar D. Parulekar, Sharad S. Sane

A Ryser design $${\mathcal {D}}$$ on v points is a collection of v proper subsets (called blocks) of a point-set with v points such that every two blocks intersect each other in $$\lambda$$ points (and $$\lambda < v$$ is a fixed number) and there are at least two block sizes. A design $${\mathcal {D}}$$ is called a symmetric design, if every point of $${\mathcal {D}}$$ has the same replication number

更新日期：2020-03-31
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-03-18
Connor Ahlbach

We introduce tableau stabilization, a new phenomenon and statistic on Young tableaux based on jeu de taquin. We investigate bounds for tableau stabilization, the shape of stabilized tableaux, and tableau stabilization as a permutation statistic. We apply tableau stabilization to construct the sufficiently large rectangular tableaux fixed by powers of promotion, which were counted by Brendon Rhoades

更新日期：2020-03-18
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-02-28
Josep Àlvarez Montaner, Fatemeh Sohrabi

We develop splitting techniques to study the Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally, we are able to compute all the Bass numbers and the shape of the injective resolution of local cohomology modules by considering the connected components of all the induced subgraphs

更新日期：2020-02-28
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-02-21
Y. S. Kwon, A. D. Mednykh, I. A. Mednykh

In the present paper, we investigate the complexity of infinite family of graphs $$H_n=H_n(G_1,\,G_2,\ldots ,G_m)$$ obtained as a circulant foliation over a graph H on m vertices with fibers $$G_1,\,G_2,\ldots ,G_m.$$ Each fiber $$G_i=C_n(s_{i,1},\,s_{i,2},\ldots ,s_{i,k_i})$$ of this foliation is the circulant graph on n vertices with jumps $$s_{i,1},\,s_{i,2},\ldots ,s_{i,k_i}.$$ This family includes

更新日期：2020-02-21
• J. Algebraic Comb. (IF 0.805) Pub Date : 2020-02-20
Behnam Khosravi, Behrooz Khosravi, Bahman Khosravi

In 1982, Babai and Godsil conjectured that almost all Cayley digraphs are digraphical regular representations. In 1998, Xu conjectured that almost all Cayley digraphs are normal [i.e., $$G_L$$ is a normal subgroup of the automorphism group of $$\text {Cay}(G,C)$$]. Finally, in 1994, Praeger and Mckay conjectured that almost all undirected vertex-transitive graphs are Cayley graphs of groups. In this

更新日期：2020-02-20
• J. Algebraic Comb. (IF 0.805) Pub Date : 2019-12-02
Ethan Berkove, Grant S. Lakeland, Alexander D. Rahm

We establish a dimension formula involving a number of parameters for the mod 2 cohomology of finite index subgroups in the Bianchi groups (SL$$_2$$ groups over the ring of integers in an imaginary quadratic number field). The proof of our formula involves an analysis of the equivariant spectral sequence, combined with torsion subcomplex reduction. We also provide an algorithm to compute a Ford domain

更新日期：2019-12-02
• J. Algebraic Comb. (IF 0.805) Pub Date : 2019-11-07
Henry Kvinge, Can Ozan Oğuz, Michael Reeks

We establish an isomorphism between the center of the twisted Heisenberg category and the subalgebra $$\Gamma$$ of the symmetric functions generated by odd power sums. We give a graphical description of the factorial Schur Q-functions and inhomogeneous power sums as closed diagrams in the twisted Heisenberg category and show that the bubble generators of the center correspond to two sets of generators

更新日期：2019-11-07
• J. Algebraic Comb. (IF 0.805) Pub Date : 2019-11-04
Dmitri I. Panyushev

Let $${{\mathfrak {g}}}$$ be a simple Lie algebra with a Borel subalgebra $${{\mathfrak {b}}}$$. Let $$\Delta ^+$$ be the corresponding (po)set of positive roots and $$\theta$$ the highest root. A pair $$\{\eta ,\eta '\}\subset \Delta ^+$$ is said to be glorious, if $$\eta ,\eta '$$ are incomparable and $$\eta +\eta '=\theta$$. Using the theory of abelian ideals of $${{\mathfrak {b}}}$$, we (1) establish

更新日期：2019-11-04
• J. Algebraic Comb. (IF 0.805) Pub Date : 2019-10-30
Ramón Flores, Juan González-Meneses

The language of maximal lexicographic representatives of elements in the positive braid monoid $$A_n$$ with n generators is a regular language. We describe with great detail the smallest finite-state automaton accepting such language and study the proportion of elements of length k whose maximal lexicographic representative finishes with the first generator. This proportion tends to some number \(P_{n

更新日期：2019-10-30
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