Pattern Avoidance in Poset Permutations

Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on P that avoid the pattern p is denoted A v P (p). We extend a proof of Simion and Schmidt to show that A v P (132)=A v P (1...

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Bibliographic Details
Main Authors: Hopkins, Samuel Francis (Contributor), Weiler, Morgan (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Springer Netherlands, 2016-07-20T15:29:38Z.
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Summary:We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on P that avoid the pattern p is denoted A v P (p). We extend a proof of Simion and Schmidt to show that A v P (132)=A v P (123) for any poset P, and we exactly classify the posets for which equality holds.
National Science Foundation (U.S.) (NSF grant 1004624)

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