Abstract
A binary relation defined on a set containing n elements can be interpreted as an n × n incidence matrix. Such matrix may be taken either over the two element boolean algebra or over the field Z2 . The main purpose of this paper is to study the incidence subgroups and the collineation subgroups of semigroups of binary relations. In doing so we shall not only obtain a partial solution to Ryser’s Conjecture (see [13], p. 123) but we shall also obtain some combinatorial results concerning the incidence subsemigroups of semigroups of binary relations.
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