Linear extensions of orderings

Vítězslav Novák; Miroslav Novotný

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 4, page 853-864
  • ISSN: 0011-4642

Abstract

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A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.

How to cite

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Novák, Vítězslav, and Novotný, Miroslav. "Linear extensions of orderings." Czechoslovak Mathematical Journal 50.4 (2000): 853-864. <http://eudml.org/doc/30605>.

@article{Novák2000,
abstract = {A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.},
author = {Novák, Vítězslav, Novotný, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {ordered set; linear extension; natural representation; lexicographic sum; dense subset; ordered set; linear extension; natural representation; lexicographic sum; dense subset},
language = {eng},
number = {4},
pages = {853-864},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear extensions of orderings},
url = {http://eudml.org/doc/30605},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Novák, Vítězslav
AU - Novotný, Miroslav
TI - Linear extensions of orderings
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 853
EP - 864
AB - A construction is given which makes it possible to find all linear extensions of a given ordered set and, conversely, to find all orderings on a given set with a prescribed linear extension. Further, dense subsets of ordered sets are studied and a procedure is presented which extends a linear extension constructed on a dense subset to the whole set.
LA - eng
KW - ordered set; linear extension; natural representation; lexicographic sum; dense subset; ordered set; linear extension; natural representation; lexicographic sum; dense subset
UR - http://eudml.org/doc/30605
ER -

References

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