Transitivity and partial order

Jiří Klaška

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 1, page 75-82
  • ISSN: 0862-7959

Abstract

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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 .

How to cite

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Klaška, Jiří. "Transitivity and partial order." Mathematica Bohemica 122.1 (1997): 75-82. <http://eudml.org/doc/248132>.

@article{Klaška1997,
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 $n=14$.},
author = {Klaška, Jiří},
journal = {Mathematica Bohemica},
keywords = {enumeration; transitivity; partial order; enumeration; transitivity; partial order},
language = {eng},
number = {1},
pages = {75-82},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Transitivity and partial order},
url = {http://eudml.org/doc/248132},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Klaška, Jiří
TI - Transitivity and partial order
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 1
SP - 75
EP - 82
AB - 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 $n=14$.
LA - eng
KW - enumeration; transitivity; partial order; enumeration; transitivity; partial order
UR - http://eudml.org/doc/248132
ER -

References

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  2. Z. I. Borevich, A comparison for the number of finite labeled T 0 -topologies, Mat. Issled. (1982), no. 65, 9-16. (In Russian.) (1982) MR0669739
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  6. K. H. Kim аnd F. W. Roush, Posets and finite topologies, Pure Appl. Math. Sci. 14 (1981), no. 1-2, 9-22. (1981) MR0613626
  7. J. Klаškа, Partitions and partially ordered sets, Acta Math. Inform. Univ. Ostraviensis 3 (1995), 45-54. (1995) MR1474065
  8. D. Kleitmаn аnd B. Rothschild, 10.1090/S0002-9947-1975-0369090-9, Trans. Amer. Math. Soc. 205 (1975), 205-220. (1975) MR0369090DOI10.1090/S0002-9947-1975-0369090-9
  9. V. Novák аnd M. Novotný, Transitive ternary relations and quasiorderings, Arch. Math. (Brno) 25 (1989), no. 1-2, 5-12. (1989) MR1189193
  10. V. Novák аnd M. Novotný, Binaгy and teгnary relations, Math. Bohem. 117 (1992), no. 3, 283-292. (1992) 

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