Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints Graham Russell Gao Hodges and empire-critical

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Groups, Graphs, and Hypergraphs: Average Sizes of Kernels of Generic Matrices with Support Constraints Graham Russell Gao Hodges and empire-criticalWe 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