Intervals of permutations with a fixed number of descents are shellable

Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604, 2016. Intervals of permutations with a fixed number of descents are shellable. Discrete Mathematics, 339 (1), pp. 118-126. ISSN 0012-365X

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Abstract

The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the Möbius function of these intervals. We present an alternative proof for a result on the Möbius function of intervals [1, π] such that π has exactly one descent. We prove that if π has exactly one descent and avoids 456123 and 356124, then the intervals [1, π] have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable.

Item Type:	Journal article
Publication Title:	Discrete Mathematics
Creators:	Smith, J.P.
Publisher:	Elsevier
Date:	6 January 2016
Volume:	339
Number:	1
ISSN:	0012-365X
Identifiers:	Number Type 10.1016/j.disc.2015.08.004 DOI S0012365X15002897 Publisher Item Identifier 1390803 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	21 Apr 2021 09:28
Last Modified:	17 Jan 2022 14:20
URI:	https://irep.ntu.ac.uk/id/eprint/42730

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