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On the Spectrum of the Derangement Graph

Renteln, Paul (2007) On the Spectrum of the Derangement Graph. Electronic Journal of Combinatorics, 14 (1). R82. ISSN 1077-8926. doi:10.37236/1000.

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We derive several interesting formulae for the eigenvalues of the derangement graph and use them to settle affirmatively a conjecture of Ku regarding the least eigenvalue.

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Additional Information:© 2007 The Author(s). Submitted: April 10, 2007; Accepted: November 1, 2007; Published: November 28, 2007. I would like to thank Cheng Ku for bringing his conjecture to my attention and for many stimulating discussions, David Wales for pointing out a discrepancy in an earlier draft, Rick Wilson and the mathematics department of the California Institute of Technology for their kind hospitality, and the referee for suggesting several improvements in the exposition.
Subject Keywords:Cayley Graph, Least Eigenvalue, Derangement Graph, Symmetric Group, Symmetric Function Theory, Complete Symmetric Factorial Functions, Shifted Schur Functions
Issue or Number:1
Record Number:CaltechAUTHORS:RENejc07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9533
Deposited By: Archive Administrator
Deposited On:30 Jan 2008
Last Modified:08 Nov 2021 21:00

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