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Keywords:
ordered set; linear extension; natural representation; lexicographic sum; dense subset
ordered set; linear extension; natural representation; lexicographic sum; dense subset
Summary:
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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