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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)
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$k$-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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