Geodesic
Linear extensions of orderings
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 853-864.

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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.
Classification : 06A06
Keywords: ordered set; linear extension; natural representation; lexicographic sum; dense subset 
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     title = {Linear extensions of orderings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {853--864},
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}
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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/