On the Möbius Function of Permutations With One Descent release_um3m3brgrzgq3jdmqmyurvfqqa

by Jason P Smith

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2014  

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.
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Date   2014-04-02
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arXiv  1306.5926v3
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