Alternating sign property of the perfect matching derangement graph
It was conjectured in the monograph [9] by Godsil and Meagher and in the article [10] by Lindzey that the perfect matching derangement graph M2n possesses the alternating sign property, that is, for any integer partition λ=(λ1,…,λr)⊢n, the sign of the eigenvalue ηλ of M2n is given by sign(ηλ)=(−1)n−...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/164642 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | It was conjectured in the monograph [9] by Godsil and Meagher and in the article [10] by Lindzey that the perfect matching derangement graph M2n possesses the alternating sign property, that is, for any integer partition λ=(λ1,…,λr)⊢n, the sign of the eigenvalue ηλ of M2n is given by sign(ηλ)=(−1)n−λ1. In this paper, we prove that the conjecture 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. |
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