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Smith, J.P. 
ORCID: 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 | ||||||||
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| Publication Title: | Discrete Mathematics | ||||||||
| Creators: | Smith, J.P. | ||||||||
| Publisher: | Elsevier | ||||||||
| Date: | 6 January 2016 | ||||||||
| Volume: | 339 | ||||||||
| Number: | 1 | ||||||||
| ISSN: | 0012-365X | ||||||||
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| 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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