Emmy-Noether-Seminar: Two edge coloring problems in algebraic combinatorics

Two edge coloring problems in algebraic combinatorics

Robert Donley (New York)

Abstract: This talk concerns two edge coloring problems, one for simplices and one for hypercubes. For simplices, we consider Stanley’s conjecture on the existence of a symmetric chain order for the restricted Young lattices $L(m, n).$ Using weak compositions, we recast the problem in terms of root systems of type A. For hypercubes, we give an overview of adinkras in supersymmetry, considered from the point of view of combinatorial designs, including perfect matchings and 1-factorizations. We give a new characterization of adinkras using Latin rectangles.