# zbMATH — the first resource for mathematics

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
##### MSC:
 05B30 Other designs, configurations 20N05 Loops, quasigroups
##### Keywords:
space nets; configuration; regularity; 4-tuples; quasigroup
Full Text: