T�tulo: Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints
Editor: American Mathematical Society
Idioma: Ingl�s
ISBN 10: 1470468689
ISBN 13: 9781470468682
Encuadernaci�n: Paperback / softback
Estado: New
Peso: 118 gramos

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Sinopsis

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 F_q-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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Tobias Rossmann, University of Galway, Ireland.

Christopher Voll, Universitat Bielefeld, Germany.

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