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arXiv · 2110.10000

The interval posets of permutations seen from the decomposition tree perspective

Mathilde Bouvel·Lapo Cioni·Benjamin Izart
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Abstract

The interval poset of a permutation is the set of intervals of a permutation, ordered with respect to inclusion. It has been introduced and studied recently in [B. Tenner, arXiv:2007.06142]. We study this poset from the perspective of the decomposition trees of permutations, describing a procedure to obtain the former from the latter. We then give alternative proofs of some of the results in [B. Tenner, arXiv:2007.06142], and we solve the open problems that it posed (and some other enumerative problems) using techniques from symbolic and analytic combinatorics. Finally, we compute the M\"obius function on such posets.

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Mathilde Bouvel, Lapo Cioni, Benjamin Izart. 2021-10-19. The interval posets of permutations seen from the decomposition tree perspective. https://arxiv.org/abs/2110.10000

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