Reiner, V. Stanton, D.
Published in
Journal of Algebraic Combinatorics

The centered difference of principally specialized Schur functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$s_{\tilde \lambda } (1,q, \ldots ,q^n ) - q^n s_{\ti...

Hobart, S. Ito, T.
Published in
Journal of Algebraic Combinatorics

Building on the work of Terwilliger, we find the structure of nonthin irreducible T-modules of endpoint 1 for P- and Q-polynomial association schemes with classical parameters. The isomorphism class of such a given module is determined by the intersection numbers of the scheme and one additional parameter which must be an eigenvalue for the first s...

Dickie, Garth A. Terwilliger, Paul M.
Published in
Journal of Algebraic Combinatorics

Let Y denote a d-class symmetric association scheme, with d ≥ 3. We show the following: If Y admits a P-polynomial structure with intersection numbers pijh and Y is 1-thin with respect to at least one vertex, then plll=0 → plii=0 1 ≤ i ≤ - 1. If Y admits a Q-polynomial structure with Krein parameters qijh, and Y is dual 1-thin with respect to at le...

Herscovici, David Samuel
Published in
Journal of Algebraic Combinatorics

In a ranked lattice, we consider two maximal chains, or “flags” to be i-adjacent if they are equal except possibly on rank i. Thus, a finite rank lattice is a chamber system. If the lattice is semimodular, as noted in [9], there is a “Jordan-Hölder permutation” between any two flags. This permutation has the properties of an Sn-distance function on...

Herscovici, David Samuel
Published in
Journal of Algebraic Combinatorics

We study paths between maximal chains, or “flags,” in finite rank semimodular lattices. Two flags are adjacent if they differ on at most one rank. A path is a sequence of flags in which consecutive flags are adjacent. We study the union of all flags on at least one minimum length path connecting two flags in the lattice. This is a subposet of the o...

Muzychuk, Mikhail
Published in
Journal of Algebraic Combinatorics

Let D be a (v,k,λ) difference set over an abelian group G with even n = k - λ. Assume that t ∈ N satisfies the congruences t ≡ qifi (mod exp(G)) for each prime divisor qi of n/2 and some integer fi. In [4] it was shown that t is a multiplier of D provided that n > λ, (n/2, λ) = 1 and (n/2, v) = 1. In this paper we show that the condition n > λ may ...

Blass, Andreas Sagan, Bruce E.
Published in
Journal of Algebraic Combinatorics

Let A be a subspace arrangement and let χ(A,t) be the characteristic polynomial of its intersection lattice L( A). We show that if the subspaces in A are taken from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlen...

Suzuki, Hiroshi
Published in
Journal of Algebraic Combinatorics

It is well known that an association scheme \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{X} = (X,\{ R_i \} _{0 \leqslant i \leqslant d} ) $$ \end{document}...

Tomiyama, Masato
Published in
Journal of Algebraic Combinatorics

Let Γ be a distance-regular graph with diameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$d \geqslant 3 $$ \end{document} and height \documentclass[12pt]{minimal...

Shor, P.W. Sloane, N.J.A.
Published in
Journal of Algebraic Combinatorics

A remarkable coincidence has led to the discovery of a family of packings of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$m^2 + m - 2{\text{ }}m/2 $$ \end{document}...