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The interval posets of permutations seen from the decomposition tree perspective

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arxiv 2110.10000 v5 pith:SME4LT6I submitted 2021-10-19 math.CO

classification math.CO
keywords arxivdecompositionintervalpermutationpermutationsperspectiveposetposets
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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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  1. Sperner's colorings of hypergraphs arising from edgewise triangulations

    math.CO 2025-06 conditional novelty 7.0 of 10

    For most permutation types of simplex-lattice hypergraphs, a new distance coloring produces more monochromatic cells than the greedy coloring, and it is optimal for a specific family.

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