The poset of mesh patterns

Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604 and Ulfarsson, H, 2020. The poset of mesh patterns. Discrete Mathematics, 343 (6): 111848. ISSN 0012-365X

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Abstract

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 µ (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.

Item Type:	Journal article
Publication Title:	Discrete Mathematics
Creators:	Smith, J.P. and Ulfarsson, H.
Publisher:	Elsevier
Date:	June 2020
Volume:	343
Number:	6
ISSN:	0012-365X
Identifiers:	Number Type 10.1016/j.disc.2020.111848 DOI S0012365X2030039X Publisher Item Identifier 1390809 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	21 Apr 2021 08:57
Last Modified:	14 Jan 2022 11:09
URI:	https://irep.ntu.ac.uk/id/eprint/42728

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