Published in Journal of Algebraic Combinatorics
We establish a relation between the Sprague–Grundy function of p-saturations of Welter’s game and the degrees of the ordinary irreducible representations of symmetric groups. In these games, a position can be regarded as a partition λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \...
Published in Journal of Algebraic Combinatorics
Let G be a finite group acting linearly on a vector space V. We consider the linear symmetry groups GL(Gv)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {GL}}(G...
Published in Journal of Algebraic Combinatorics
There has been much research on (pa,pb,pa,pa-b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p^{a},p^{b},p^{a},p^{a-b})$$\end{document} relative difference sets with...
Published in Journal of Algebraic Combinatorics
If g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {g}$$\end{document} is a Frobenius Lie algebra, then for certain F∈g∗\documentclass[12pt]{minimal} \usepac...
Published in Journal of Algebraic Combinatorics
Let Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} denote a bipartite distance-regular graph with vertex set X, diameter D≥4\documentclass[12p...
Published in Journal of Algebraic Combinatorics
We establish, for the character table of the symmetric group, the positivity of the row sums indexed by irreducible characters, when restricted to various subsets of the conjugacy classes. A notable example is that of partitions with all parts odd. More generally, we study representations related to the conjugacy action of the symmetric group. Thes...
Published in Journal of Algebraic Combinatorics
In recent work we constructed two new near octagons, one related to the finite simple group G2(4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {G}_2(4)$$\end{...
Published in Journal of Algebraic Combinatorics
The critical group of a finite graph is an abelian group defined by the Smith normal form of the Laplacian. We determine the critical groups of the Peisert graphs, a certain family of strongly regular graphs similar to, but different from, the Paley graphs. It is further shown that the adjacency matrices of the two graphs defined over a field of or...
Published in Journal of Algebraic Combinatorics
It was proven by González-Meneses, Manchón and Silvero that the extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex obtained from a bipartite circle graph constructed from the diagram. In this paper, we conjecture that this simplicial complex is always homotopy equivalent to a...
Published in Journal of Algebraic Combinatorics
Let Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varGamma $$\end{document} be a distance-semiregular graph on Y, and let DY\documentclass[12pt]{minimal} \usepackag...
