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Configuration in space nets. (Russian) Zbl 0557.05022
In this paper an attempt is made to construct a general theory of configurations in space nets. In particular, it is proved that for each connected configuration M(n,m,4) - (m is the number of vertices, n is the number of different faces of the configuration) with regularity 4 the following inequalities hold 1. 3/4n\(\leq m\leq n(n-1)/6\), 2. \(3\leq \rho (a)<(4/j)m\) where a is an arbitrary face, \(\rho\) (a) is the number of vertices of the face a. The notions of special system of 4-tuples and partial TS-3-quasigroup are introduced and some questions concerning isomorphism and interconnection between them are studied.
Reviewer: S.S.Agayan
05B30 Other designs, configurations
20N05 Loops, quasigroups
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