Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints - Couverture souple

Rossmann, Tobias; Voll, Christopher

 
9781470468682: Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints
Couverture souple
ISBN 10 : 1470468689 ISBN 13 : 9781470468682
Editeur : American Mathematical Society, 2024

Synopsis

We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish strong uniformity results pertaining to zeta functions enumerating conjugacy classes of these groups. We deduce that the numbers of conjugacy classes of Fq-points of the groups under consideration depend polynomially on q. Our approach combines group theory, graph theory, toric geometry, and p-adic integration.

Our uniformity results are in line with a conjecture of Higman on the numbers of conjugacy classes of unitriangular matrix groups. Our findings are, however, in stark contrast to related results by Belkale and Brosnan on the numbers of generic symmetric matrices of given rank associated with graphs.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Tobias Rossmann, University of Galway, Ireland.

Christopher Voll, Universitat Bielefeld, Germany.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2024
Langue
anglais
ISBN 10 
1470468689
ISBN 13 
9781470468682
Reliure
Broché
Nombre de pages
120
Coordonnées du fabricant
non disponible
Personne responsable
non disponible