Journal Article10.1007/BF00383444
Counting linear extensions
Graham Brightwell,Peter Winkler +1 more
346
TL;DR: The problem of counting the number of linear extensions of a partially ordered set is #P-complete as discussed by the authors, which is the state-of-the-art algorithm for this problem.
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Abstract: We survey the problem of counting the number of linear extensions of a partially ordered set. We show that this problem is #P-complete, settling a long-standing open question. This result is contrasted with recent work giving randomized polynomial-time algorithms for estimating the number of linear extensions.
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