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Pattern Avoidance in Poset Permutations

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Abstract

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.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Morgan Weiler

  2. University of California, Berkeley, Berkeley, CA, 94704, USA

    Sam Hopkins

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  1. Sam Hopkins
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  2. Morgan Weiler
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Correspondence to Morgan Weiler.

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Hopkins, S., Weiler, M. Pattern Avoidance in Poset Permutations. Order 33, 299–310 (2016). https://doi.org/10.1007/s11083-015-9367-7

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  • DOI: https://doi.org/10.1007/s11083-015-9367-7

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