Geodesic
Linear extensions of orderings
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 853-864 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06A06
Keywords: ordered set; linear extension; natural representation; lexicographic sum; dense subset 
@article{CMJ_2000_50_4_a12,
     author = {Nov\'ak, V{\'\i}t\v{e}zslav and Novotn\'y, Miroslav},
     title = {Linear extensions of orderings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {853--864},
     year = {2000},
     volume = {50},
     number = {4},
     mrnumber = {1792975},
     zbl = {1079.06500},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a12/}
}
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Novák, Vítězslav; Novotný, Miroslav. Linear extensions of orderings. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 853-864. http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a12/