Linear extensions of orderings |
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| Authors: | Vítězslav Novák Miroslav Novotný |
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| Affiliation: | (1) Department of Mathematics, Masaryk University, Janá!["ccaron"]("/content/l441071q4676k482/xlarge269.gif") kovo nám. 2a, 662 95 Brno, Czech Republic;(2) Faculty of Computer Science, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic |
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| 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. |
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| Keywords: | ordered set linear extension natural representation lexicographic sum dense subset |
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