On the Möbius function of permutations with one descent

Smith, JP ORCID: https://orcid.org/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
Identifiers:	Number Type 10.37236/3559 DOI 1390806 Other
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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