Alternating sign property of the perfect matching derangement graph

Document Type

Article

Publication Date

2-1-2023

Abstract

It was conjectured in the monograph 9] by Godsil and Meagher and in the article 10] by Lindzey that the per-fect matching derangement graph M2n possesses the alter-nating sign property, that is, for any integer partition A = (A1, . . . , Ar) diamond -n, the sign of the eigenvalue eta lambda of M2n is given by sign(eta lambda) = (-1)n-lambda 1 . In this paper, we prove that the con-jecture is true. Our approach yields a recurrence formula for the eigenvalues of the perfect matching derangement graph as well as a new recurrence formula for the eigenvalues of the permutation derangement graph.(c) 2022 Elsevier Inc. All rights reserved.

Keywords

Association schemes, Perfect matchings, Erd?s-Ko-Rado, Jack polynomials, Derangements

Publication Title

Journal of Combinatorial Theory, Series A

Divisions

MathematicalSciences

Volume

194

Publisher

Elsevier

Publisher Location

525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA

This document is currently not available here.

Share

COinS