Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints: Volume: 294 Number: 1465 - Brossura

Rossmann, Tobias; Voll, Christopher

 
9781470468682: Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints: Volume: 294 Number: 1465
Brossura
ISBN 10: 1470468689 ISBN 13: 9781470468682
Casa editrice: American Mathematical Society, 2024

Sinossi

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.

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Editore
American Mathematical Society
Data di pubblicazione
2024
Lingua
Inglese
ISBN 10 
1470468689
ISBN 13 
9781470468682
Rilegatura
Copertina flessibile
Numero di pagine
120
Contatto del produttore
non disponibile
Persona responsabile
non disponibile