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

 
9781470468682: Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints

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Tobias Rossmann, Tobias Rossmann
ISBN 10: 1470468689 ISBN 13: 9781470468682
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Tobias Rossmann, Christopher Voll
ISBN 10: 1470468689 ISBN 13: 9781470468682
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Paperback. Condition: New. 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. Seller Inventory # LU-9781470468682

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Rossmann, Tobias (Author)/ Voll, Christopher (Author)
Published by American Mathematical Society, 2024
ISBN 10: 1470468689 ISBN 13: 9781470468682
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Tobias Rossmann
Published by MP-AMM American Mathematical, 2024
ISBN 10: 1470468689 ISBN 13: 9781470468682
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Tobias Rossmann, Tobias Rossmann
ISBN 10: 1470468689 ISBN 13: 9781470468682
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ISBN 10: 1470468689 ISBN 13: 9781470468682
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ISBN 10: 1470468689 ISBN 13: 9781470468682
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Paperback. Condition: New. 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. Seller Inventory # LU-9781470468682

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