Work

Binomial Cayley graphs and applications to dynamics on finite spaces

Year: 2024

Type: 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.

Source: Algebraic Combinatorics

DOI: 10.5802/alco.361

Authors: Bernat Bassols Cornudella, Francesco Viganò

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Imperial College London, University College London, Engineering and Physical Sciences Research Council

Awards: EPSRC Centre for Doctoral Training in Geometry and Number Theory at the Interface: London School of Geometry and Number Theory, G1600321425, G3041038843, G3262250305, EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation

OpenAlex ID: W4402190127