This article is cited in 2 papers

Mathematical logic, algebra and number theory

Combinatorial problems connected with P. Hall's collection process

V. M. Leontiev

Institute of Mathematics and Computer Science, Siberian Federal University, 79, Svobodny ave., Krasnoyarsk, 660041, Russia

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 the number of elements $(\lambda_1, \ldots, \lambda_r) \in M_1 \times \cdots \times M_r$ that satisfy the condition $C$, where $C$ is a propositional formula consisting of such conditions as $\lambda_i=\lambda_j$, $\lambda_i<\lambda_j$, $i,j \in \overline{1,r}$.

Keywords: collection process, Cartesian product, binary weight.

UDC: 519.117, 519.156, 519.11

MSC: 05A99

Received August 7, 2019, published June 30, 2020

DOI: 10.33048/semi.2020.17.064

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