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  • Tropical curves of hyperelliptic type
    J. Algebraic Comb. (IF 0.854) 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 0.854) 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 0.854) 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
  • Vertex-minimal planar graphs with a prescribed automorphism group
    J. Algebraic Comb. (IF 0.854) 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
  • Complexity of shift spaces on semigroups
    J. Algebraic Comb. (IF 0.854) 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
  • k -partial permutations and the center of the wreath product $${\mathcal {S}}_k\wr {\mathcal {S}}_n$$Sk≀Sn algebra
    J. Algebraic Comb. (IF 0.854) 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
  • Tropical hyperelliptic curves in the plane
    J. Algebraic Comb. (IF 0.854) 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
  • A note on some new hook-content identities
    J. Algebraic Comb. (IF 0.854) 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
  • Braided dendriform and tridendriform algebras, and braided Hopf algebras of rooted trees
    J. Algebraic Comb. (IF 0.854) 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
  • LLT polynomials, elementary symmetric functions and melting lollipops
    J. Algebraic Comb. (IF 0.854) 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
  • Cayley graphs with few automorphisms
    J. Algebraic Comb. (IF 0.854) 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
  • Some results on the Ryser design conjecture-III
    J. Algebraic Comb. (IF 0.854) 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
  • Tableau stabilization and rectangular tableaux fixed by promotion powers
    J. Algebraic Comb. (IF 0.854) 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
  • Bass numbers of local cohomology of cover ideals of graphs
    J. Algebraic Comb. (IF 0.854) 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
  • Complexity of the circulant foliation over a graph
    J. Algebraic Comb. (IF 0.854) 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
  • On the automorphism groups of vertex-transitive Cayley digraphs of monoids
    J. Algebraic Comb. (IF 0.854) 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
  • Syzygies of the apolar ideals of the determinant and permanent
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-06-04
    Jarod Alper, Rowan Rowlands

    We investigate the space of syzygies of the apolar ideals \({\text {det}}_n^\perp \) and \({\mathrm{perm}}_n^\perp \) of the determinant \({\text {det}}_n\) and permanent \({\mathrm{perm}}_n\) polynomials. Shafiei had proved that these ideals are generated by quadrics and provided a minimal generating set. Extending on her work, in characteristic distinct from two, we prove that the space of relations

    更新日期:2019-06-04
  • New identities for terminating balanced $$_4\phi _3$$4ϕ3 -series
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-06-03
    Xiaojing Chen, Wenchang Chu

    The duplicate form of the Carlitz inversions is employed to prove new identities for terminating balanced \(_4\phi _3\)-series. Their limiting series are deduced as consequences. The “dual formulae” are also derived by means of the polynomial argument.

    更新日期:2019-06-03
  • On the combinatorics of the Hopf algebra of dissection diagrams
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-25
    Cécile Mammez

    In this article, we study the Hopf algebra \(\mathcal {H}_{\tiny \textsc {D}}\) of dissection diagrams introduced by Dupont in his thesis, more precisely we focus on its underlying coalgebra. We use the version with a parameter x in the base field. We conjecture it is cofree if \(x=1\) or x is not a root of unity. If \(x=-1\), then we know there is no cofreeness. Since \(\mathcal {H}_{\tiny \textsc

    更新日期:2019-05-25
  • Automorphisms and isomorphisms of some p -ary bent functions
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-23
    Ulrich Dempwolff

    In the predecessor to this paper Dempwolff (Comm Algebra 34(3):1077–1131, 2006), group-theoretic methods were used to solve automorphism and equivalence questions for (certain) ordinary bent functions, i.e., bent functions over \(\mathbb {F}_2\). Here, we consider the same problems for p-ary bent functions, p an odd prime and solve these questions for functions analogous to those which appear in Dempwolff

    更新日期:2019-05-23
  • A combinatorial method for computing characteristic polynomials of starlike hypergraphs
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-22
    Yan-Hong Bao, Yi-Zheng Fan, Yi Wang, Ming Zhu

    Using the Poisson formula for resultants, and variants of the chip-firing game on graphs, we provide a combinatorial method for computing a class of resultants corresponding to the characteristic polynomials of the adjacency tensors of starlike hypergraphs including hyperpaths and hyperstars, which are given recursively and explicitly.

    更新日期:2019-05-22
  • Polarization and depolarization of monomial ideals with application to multi-state system reliability
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-21
    Fatemeh Mohammadi, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón, Henry P. Wynn

    Polarization is a powerful technique in algebra which provides combinatorial tools to study algebraic invariants of monomial ideals. We study the reverse of this process, depolarization which leads to a family of ideals which share many common features with the original ideal. Given a squarefree monomial ideal, we describe a combinatorial method to obtain all its depolarizations, and we highlight their

    更新日期:2019-05-21
  • The complex $$K^{*}$$K∗ ring of the complex projective Stiefel manifold
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-20
    Shilpa Gondhali

    The topological \(K^{*}\) ring is one of the important tools used for understanding the topology of a manifold. We settle a problem of computing the \(K^{*}\) ring of complex projective Stiefel manifold using combinatorics. We calculate \(K^{*}\) ring of the right generalized projective Stiefel manifold, denoted by \(P_{\ell }W_{n,k}\) , which gives us description of complex \(K^{*}\) ring of complex

    更新日期:2019-05-20
  • Hopf algebras of planar binary trees: an operated algebra approach
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-20
    Yi Zhang, Xing Gao

    Parallel to operated algebras built on top of planar rooted trees via the grafting operator \(B^+\), we introduce and study \(\vee \)-algebras and more generally \(\vee _\Omega \)-algebras based on planar binary trees. Involving an analogy of the Hochschild 1-cocycle condition, cocycle \(\vee _\Omega \)-bialgebras (resp. \(\vee _\Omega \)-Hopf algebras) are also introduced and their free objects are

    更新日期:2019-05-20
  • On some distance-regular graphs with many vertices
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-05-18
    Dean Crnković, Sanja Rukavina, Andrea Švob

    We construct distance-regular graphs, including strongly regular graphs, admitting a transitive action of the Chevalley groups \(G_2(4)\) and \(G_2(5)\), the orthogonal group O(7, 3) and the Tits group \(T=\)\(^2F_4(2)'\). Most of the constructed graphs have more than 1000 vertices, and the number of vertices goes up to 28431. Some of the obtained graphs are new.

    更新日期:2019-05-18
  • Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-04-09
    František Marko

    Let \(G=GL(m|n)\) be the general linear supergroup over an algebraically closed field K of characteristic zero, and let \(G_{ev}=GL(m)\times GL(n)\) be its even subsupergroup. The induced supermodule \(H^0_G(\lambda )\), corresponding to a dominant weight \(\lambda \) of G, can be represented as \(H^0_{G_{ev}}(\lambda )\otimes \Lambda (Y)\), where \(Y=V_m^*\otimes V_n\) is a tensor product of the dual

    更新日期:2019-04-09
  • A monoid of Kostka–Foulkes polynomials
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-04-01
    Pasquale Petrullo, Domenico Senato

    We introduce the monoid of the admissible KF polynomials. These polynomials are invariant under uniform translation of partitions. Moreover, each Kostka–Foulkes polynomial turns out to be a linear combination of admissible KF polynomials with coefficients \(-1\) or 1. Elementary manipulations of triangular matrices provide identities on Kostka–Foulkes polynomials which are not obvious a priori.

    更新日期:2019-04-01
  • Weighted quasisymmetric enumerator for generalized permutohedra
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-03-27
    Vladimir Grujić, Marko Pešović, Tanja Stojadinović

    We introduce a weighted quasisymmetric enumerator function associated with generalized permutohedra. It refines the Billera, Jia and Reiner quasisymmetric function which also includes the Stanley chromatic symmetric function. Besides that, it carries information of face numbers of generalized permutohedra. We consider more systematically the cases of nestohedra and matroid base polytopes.

    更新日期:2019-03-27
  • Equisizable partial sum families
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-03-26
    Ricardo Grande, István Kovács, Klavdija Kutnar, Aleksander Malnič, Luis Martínez, Dragan Marušič

    We introduce a special kind of partial sum families, which we call equisizable partial sum families, that can be used to obtain directed strongly regular graphs admitting a semiregular group of automorphisms. We give a construction of an infinite family of equisizable partial sum families depending on two parameters that produce directed strongly regular graphs with new parameters. We also determine

    更新日期:2019-03-26
  • New characterizations of freeness for hyperplane arrangements
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-03-26
    Anna Maria Bigatti, Elisa Palezzato, Michele Torielli

    In this article, we describe two new characterizations of freeness for hyperplane arrangements via the study of the generic initial ideal and of the sectional matrix of the Jacobian ideal of arrangements.

    更新日期:2019-03-26
  • Density function for the second coefficient of the Hilbert–Kunz function on projective toric varieties
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-03-23
    Mandira Mondal, Vijaylaxmi Trivedi

    We prove that, analogous to the Hilbert–Kunz density function, (used for studying the Hilbert–Kunz multiplicity, the leading coefficient of the Hibert–Kunz function), there exists a \(\beta \)-density function \(g_{R, \mathbf{m}}:[0,\infty )\longrightarrow {\mathbb {R}}\), where \((R, \mathbf{m})\) is the homogeneous coordinate ring associated with the toric pair (X, D), such that $$\begin{aligned}

    更新日期:2019-03-23
  • Polynomial super representations of $$U_{q}^{\mathrm{res}}(\mathfrak {gl}_{m|n})$$Uqres(glm|n) at roots of unity
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-02-02
    Jie Du, Yanan Lin, Zhongguo Zhou

    As a homomorphic image of the hyperalgebra \(U_{q,R}(m|n)\) associated with the quantum linear supergroup \(U_{\varvec{\upsilon }}(\mathfrak {gl}_{m|n})\), we first give a presentation for the q-Schur superalgebra \(S_{q,R}(m|n,r)\) over a commutative ring R. We then develop a criterion for polynomial supermodules of \(U_{q,F}(m|n)\) over a field F and use this to determine a classification of polynomial

    更新日期:2019-02-02
  • Tetravalent half-arc-transitive graphs of order 8 p
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-01-31
    Xiuyun Wang, Jihui Wang, Yan Liu

    A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let p be a prime. It is known that there exist no tetravalent half-arc-transitive graphs of order p or 2p. Feng et al. (J Algebraic Combin 26:431–451, 2007) gave the classification of tetravalent half-arc-transitive graphs of order 4p. In this paper, a classification is given of

    更新日期:2019-01-31
  • Unexpected curves arising from special line arrangements
    J. Algebraic Comb. (IF 0.854) Pub Date : 2019-01-23
    Michela Di Marca, Grzegorz Malara, Alessandro Oneto

    In a recent paper, Cook et al. (Compos Math 154:2150–2194, 2018) used the splitting type of a line arrangement in the projective plane to study the number of conditions imposed by a general fat point of multiplicity j on the linear system of curves of degree \(j+1\) passing through the configuration of points dual to the given arrangement. If the number of conditions is less than the expected, they

    更新日期:2019-01-23
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