COMBINATORIAL PROBLEMS CONNECTED WITH P. HALLS COLLECTION PROCESS

Abstract

Let M_1, \ldots, M_r be nonempty subsets of any totally ordered set. Imposing some restricitons on these subsets, we find an expression for thenumber of elements (\lambda_1, \ldots, \lambda_r) \in M_1, \ldots, M_r that satisfy the condition C, where C is a propositional formula consisting of such conditions as \lambda_i = \lambda_j , \lambda_i < \lambda_j, i,j \in \overline{1,r}.