MATHEMATICA BOHEMICA, Vol. 122, No. 1, pp. 75-82 (1997)

Transitivity and partial order

Jiri Klaska

Jiri Klaska, Department of Mathematics, Technical University Brno, Technicka 2, 616 69 Brno, Czech Republic, e-mail: klaska@mat.fme.vutbr.cz

Abstract: In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary $n$-element set up to $n=14$.

Keywords: enumeration, transitivity, partial order

Classification (MSC2000): 05A15, 06A07, 54A10

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