The poset of mesh patterns

Discrete Mathematics, Volume 343, Issue 6, June 2020

Jason and Henning

An interval We introduce the poset of mesh patterns, which generalises the permutation pattern poset. We fully classify the mesh patterns for which the interval [1,m] is non-pure, where 1 is the unshaded singleton mesh pattern. We present some results on the Möbius function of the poset, and show that its value on [1,m] is almost always zero. Finally, we introduce a class of disconnected and non-shellable intervals by generalising the direct product operation from permutations to mesh patterns.

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