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

Häftad, Engelska, 2024

Del i serien Memoirs of the American Mathematical Society

1 023 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2024-05-31
Mått:178 x 254 x undefined mm
Vikt:118 g
Format:Häftad
Språk:Engelska
Serie:Memoirs of the American Mathematical Society
Antal sidor:120
Förlag:American Mathematical Society
ISBN:9781470468682

Utforska kategorier

Mer om författaren

Tobias Rossmann, University of Galway, Ireland.Christopher Voll, Universitat Bielefeld, Germany.

Innehållsförteckning

1. Introduction2. Ask zeta functions and modules over polynomial rings3. Modules and module representations from (hyper)graphs4. Modules over toric rings and associated zeta functions5. Ask zeta functions of hypergraphs6. Uniformity for ask zeta functions of graphs7. Graph operations and ask zeta functions of cographs8. Cographs, hypergraphs, and cographical groups9. Further examples10. Open problems

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

AvTobias Rossmann,Christopher Voll

Häftad, Engelska, 2024

Del i serien Memoirs of the American Mathematical Society

1 023 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

Produktinformation

Utgivningsdatum:2024-05-31
Mått:178 x 254 x undefined mm
Vikt:118 g
Format:Häftad
Språk:Engelska
Serie:Memoirs of the American Mathematical Society
Antal sidor:120
Förlag:American Mathematical Society
ISBN:9781470468682

Utforska kategorier

Mer om författaren

Tobias Rossmann, University of Galway, Ireland.Christopher Voll, Universitat Bielefeld, Germany.

Innehållsförteckning

1. Introduction2. Ask zeta functions and modules over polynomial rings3. Modules and module representations from (hyper)graphs4. Modules over toric rings and associated zeta functions5. Ask zeta functions of hypergraphs6. Uniformity for ask zeta functions of graphs7. Graph operations and ask zeta functions of cographs8. Cographs, hypergraphs, and cographical groups9. Further examples10. Open problems

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