Asymptotic behaviour of the containment of certain mesh patterns

Govc, D and Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604, 2022. Asymptotic behaviour of the containment of certain mesh patterns. Discrete Mathematics, 345 (5): 112813. ISSN 0012-365X

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Abstract

We present some results on the proportion of permutations of length n containing certain mesh patterns as n grows large, and give exact enumeration results in some cases. In particular, we focus on mesh patterns where entire rows and columns are shaded. We prove some general results which apply to mesh patterns of any length, and then consider mesh patterns of length four. An important consequence of these results is to show that the proportion of permutations containing a mesh pattern can take a wide range of values between 0 and 1.

Item Type:	Journal article
Publication Title:	Discrete Mathematics
Creators:	Govc, D. and Smith, J.P.
Publisher:	Elsevier
Date:	May 2022
Volume:	345
Number:	5
ISSN:	0012-365X
Identifiers:	Number Type 10.1016/j.disc.2022.112813 DOI 1508755 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Jonathan Gallacher
Date Added:	19 Jan 2022 11:11
Last Modified:	20 Jan 2023 03:00
URI:	https://irep.ntu.ac.uk/id/eprint/45358

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