Combinatorial aspects of relations
A multivalued group-like system called polygroup (a special type of multigroup in the sense of \textit{M. Dresher} and \textit{Ø. Ore} [Am. J. Math. 60, 705-733 (1938; Zbl 0019.10701)] is introduced. Polygroups can be characterized as the atomic structures (under composition and reverse) of complete atomic integral relation algebras (see \textit{B. Jónsson} and \textit{A. Tarski} [ibid. 74, 127-162 (1952; Zbl 0049.15801)]. Due to this, there is a correspondence between certain properties of IRA's (such as different kinds of representability) and those of polygroups. Also, information can be obtained about automorphism groups of colour schemes (colourings of the edges of complete graphs, subject to some conditions) from the knowledge of polygroups attached to them (so called chromatic polygroups). The last two theorems give some approach to problems concerning the orbits of stabilizers of the elements in transitive permutation groups by ways of polygroups.
complete atomic integral relation algebras
scientific article; zbMATH DE number 3875564
scientific article