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Smith, J.P. 
ORCID: 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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Official URL: https://doi.org/10.1016/j.disc.2020.111848
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 | ||||||||
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| Publication Title: | Discrete Mathematics | ||||||||
| Creators: | Smith, J.P. and Ulfarsson, H. | ||||||||
| Publisher: | Elsevier | ||||||||
| Date: | June 2020 | ||||||||
| Volume: | 343 | ||||||||
| Number: | 6 | ||||||||
| ISSN: | 0012-365X | ||||||||
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| 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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