Binomial Cayley graphs and applications to dynamics on finite spaces
File(s)
Published version
Author(s)
Bassols Cornudella, Bernat
Viganò, Francesco
Type
Journal Article
Abstract
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the other with powers of cyclic groups. We determine various combinatorial properties of these graphs through the spectral analysis of their adjacency matrices. In the case of symmetric groups, we establish a relation between the multiplicity of the null eigenvalue and longest increasing sub-sequences of permutations by means of the RSK correspondence. Finally, we consider dynamical arrangements of finitely many elements in finite spaces, which we refer to as particle-box systems. We apply the results obtained on binomial Cayley graphs in order to describe their degeneracy.
Date Issued
2024-09-02
Date Acceptance
2024-02-04
Citation
Algebraic Combinatorics, 2024, 7 (4), pp.1197-1223
ISSN
2589-5486
Publisher
MathOA
Start Page
1197
End Page
1223
Journal / Book Title
Algebraic Combinatorics
Volume
7
Issue
4
Copyright Statement
© The author(s), 2024. This article is licensed under the
CREATIVE COMMONS ATTRIBUTION (CC-BY) 4.0 LICENSE.
http://creativecommons.org/licenses/by/4.0/
CREATIVE COMMONS ATTRIBUTION (CC-BY) 4.0 LICENSE.
http://creativecommons.org/licenses/by/4.0/
License URL
Identifier
https://alco.centre-mersenne.org/articles/10.5802/alco.361/
Publication Status
Published
Date Publish Online
2024-09-03