Koh, Zhi Kang Samuel and Ku, Cheng Yeaw and Wong, Kok Bin (2023) Alternating sign property of the perfect matching derangement graph. Journal of Combinatorial Theory, Series A, 194. ISSN 0097-3165, DOI https://doi.org/10.1016/j.jcta.2022.105706.
Full text not available from this repository.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.
| Item Type: | Article |
|---|---|
| Funders: | UNSPECIFIED |
| Uncontrolled Keywords: | Association schemes; Perfect matchings; Erd?s-Ko-Rado; Jack polynomials; Derangements |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms Zaharah Ramly |
| Date Deposited: | 11 Jul 2023 06:15 |
| Last Modified: | 11 Jul 2023 06:15 |
| URI: | http://eprints.um.edu.my/id/eprint/39348 |
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