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商品詳細
Groups, Graphs, and Hypergraphs : Average Sizes of Kernels of Generic Matrices with Support Constraints.
・ISBN 978-1-4704-6868-2 paper US$ 85.00
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| 著者・編者 | Rossmann, Tobias / Voll, Christopher, |
|---|---|
| シリーズ | Memoirs of the American Mathematical Society |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2024 |
| ページ数 | 120 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-5263＞ |
解説
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.
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.