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Seminar by Department of Discrete Mathematic, Steklov Mathematical Institute of RAS
September 28, 2021 16:00, Moscow, Steklov Mathematical Institute of RAS, Room 511 (8 Gubkina)
 


$k$-configurations

F. M. Malyshev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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Abstract: An overview of classification theorems and methods for constructing $k$-configurations defined by their incident matrices $L$ is given. They are nondegenerate over the field $GF(2)$. Each row and each column of the matrices $L,\,L^{-1}$ contains exactly $k$ units. To construct $k$-configurations, we use regular polyhedra, regular and symmetric graphs, quadratic residues and nonquadratic residues of finite fields, finite groups, $(v,k,\lambda)$-configurations, including perfect difference sets, finite projective planes, and Hadamard matrices.

Keywords: configurations, finite groups, symmetric graphs, regular polyhedra, surface triangulations.
 
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