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Smith, J.P. 
ORCID: 0000-0002-4209-1604,
2014.
On the Möbius function of permutations with one descent.
Electronic Journal of Combinatorics, 21 (2): P2.11.
ISSN 1077-8926
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Abstract
The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the Möbius function of intervals [1, π] in this poset, for any permutation π with at most one descent. We compute the Möbius function as a function of the number and positions of pairs of consecutive letters in π that are consecutive in value. As a result of this we show that the Möbius function is unbounded on the poset of all permutations. We show that the Möbius function is zero on any interval [1, π] where π has a triple of consecutive letters whose values are consecutive and monotone. We also conjecture values of the Möbius function on some other intervals of permutations with at most one descent.
| Item Type: | Journal article | ||||||
|---|---|---|---|---|---|---|---|
| Publication Title: | Electronic Journal of Combinatorics | ||||||
| Creators: | Smith, J.P. | ||||||
| Publisher: | Electronic Journal of Combinatorics | ||||||
| Date: | 16 April 2014 | ||||||
| Volume: | 21 | ||||||
| Number: | 2 | ||||||
| ISSN: | 1077-8926 | ||||||
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| Divisions: | Schools > School of Science and Technology | ||||||
| Record created by: | Linda Sullivan | ||||||
| Date Added: | 21 Apr 2021 09:33 | ||||||
| Last Modified: | 17 Jan 2022 13:35 | ||||||
| URI: | https://irep.ntu.ac.uk/id/eprint/42731 |
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