Eigenvalues of the Derangement Graph
Abstract
We consider the Cayley graph on the symmetric group Sn generated by derangements. It is well known that the eigenvalues of this grpah are indexed by partitions of n. We investigate how these eigenvalues are determined by the shape of their corresponding partitions. In particular, we show that the sign of an eigenvalue is the parity of the number of cells below the first row of the corresponding Ferrers diagram. We also provide some lower and upper bounds for the absolute values of these eigenvalues.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 DOI:
 10.48550/arXiv.0803.2901
 arXiv:
 arXiv:0803.2901
 Bibcode:
 2008arXiv0803.2901Y
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 05Axx;
 05Cxx
 EPrint:
 26 pages