Zhang, Tao Ge, Gennian
Published in
Journal of Algebraic Combinatorics

Let C(d, k) and AC(d, k) be the largest order of a Cayley graph and a Cayley graph based on an abelian group, respectively, of degree d and diameter k. It is well known that C(d,k)≤1+d+d(d-1)+⋯+d(d-1)k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...

Fan, Wenwen Li, Cai Heng Wang, Naer
Published in
Journal of Algebraic Combinatorics

It is shown that a bipartite multi-graph Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varGamma }$$\end{document} has an orientably edge-transitive embedding with ...

Cameron, Peter J. Guerra, Horacio Jurina, Šimon
Published in
Journal of Algebraic Combinatorics

The power graphP(G) of a group G is the graph whose vertex set is G, with x and y joined if one is a power of the other; the directed power graphP→(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemar...

Blom, Harry
Published in
Journal of Algebraic Combinatorics

Forsgård, Jens
Published in
Journal of Algebraic Combinatorics

We introduce an invariant of a finite point configuration A⊂R1+n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \subset \mathbb {R}^{1+n}$$\end{document} which we den...

Hibi, Takayuki Tsuchiya, Akiyoshi
Published in
Journal of Algebraic Combinatorics

Reflexive polytopes which have the integer decomposition property are of interest. Recently, some large classes of reflexive polytopes with integer decomposition property coming from the order polytopes and the chain polytopes of finite partially ordered sets are known. In the present paper, we will generalize this result. In fact, by virtue of the...

Kotsireas, Ilias S.
Published in
Journal of Algebraic Combinatorics

Rains, Eric M. Warnaar, S. Ole
Published in
Journal of Algebraic Combinatorics

We prove a Macdonald polynomial analogue of the celebrated Nekrasov–Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of the main conjectures of Hausel and Rodriguez-Villegas from their work on mixed Hodge polynomials of the moduli space of stable Higgs bundles on Riemann surfaces.

Gao, Yibo Zhang, YiYu
Published in
Journal of Algebraic Combinatorics

Varchenko (Adv Math 97(1):110–144, 1993) defined the Varchenko matrix associated with any real hyperplane arrangement and computed its determinant. In this paper, we show that the Varchenko matrix of a hyperplane arrangement has a diagonal form if and only if it is semigeneral, i.e., without degeneracy. In the case of semigeneral arrangement, we pr...

Doyle, John Kevin Tucker, Thomas W. Watkins, Mark E.
Published in
Journal of Algebraic Combinatorics

A Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A graphical Frobenius representation (GFR) of a Frobenius group G is a graph whose automorphism group, as a group of permutations of the vertex set, is isomorphic to G. The problem of classifying which Frobenius groups ...