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 ...

Jedwab, Jonathan Li, Shuxing
Published in
Journal of Algebraic Combinatorics

Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. We characterize the parameters (v,m,k,λ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepac...

Caviglia, Giulio Hà, Huy Tài Herzog, Jürgen Kummini, Manoj Terai, Naoki Trung, Ngo Viet
Published in
Journal of Algebraic Combinatorics

We study the relationship between depth and regularity of a homogeneous ideal I and those of (I, f) and I : f, where f is a linear form or a monomial. Our results have several interesting consequences on depth and regularity of edge ideals of hypergraphs and of powers of ideals.

Xu, Wenqin Du, Shaofei
Published in
Journal of Algebraic Combinatorics

In this paper, a complete classification is achieved of all the regular covers of the complete bipartite graphs Kn,n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{n...

Abdallah, Nancy Hultman, Axel
Published in
Journal of Algebraic Combinatorics

When Sp(2n,C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Sp}(2n,\mathbb {C})$$\end{document} acts on the flag variety of SL(2n,C)\documentclass[12pt]{minim...

Bishnoi, A. De Bruyn, B.
Published in
Journal of Algebraic Combinatorics

In recent work we constructed two new near octagons, one related to the finite simple group G2(4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {G}_2(4)$$\end{...

Thas, Koen
Published in
Journal of Algebraic Combinatorics

Modulo a combination of duality, translation duality or Payne integration, every known finite generalized quadrangle except for the Hermitian quadrangles H(4,q2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...

Alfuraidan, M. R. Hall, J. I. Laradji, A.
Published in
Journal of Algebraic Combinatorics

In an earlier paper, the first two authors found all distance-regular antipodal covers of all known primitive distance-transitive graphs of diameter at least 3 with one possible exception. That remaining case is resolved here with the proof that a primitive and distance-transitive collinearity graph of a finite generalized 2d-gon with d≥3\documentc...