Geodesic
Transitivity and partial order
Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 75-82

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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 $n=14$.
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 $n=14$.
DOI : 10.21136/MB.1997.126183
Classification : 04A05, 05A15, 06A07, 54A10
Keywords: enumeration; transitivity; partial order 
Klaška, Jiří. Transitivity and partial order. Mathematica Bohemica, Tome 122 (1997) no. 1, pp. 75-82. doi: 10.21136/MB.1997.126183
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