Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2021

An order on circular permutations

Un ordre sur les permutations circulaires

Résumé

Motivation coming from the study of affine Weyl groups, a structure of ranked poset is defined on the set of circular permutations in $S_n$ (that is, $n$-cycles). It is isomorphic to the poset of so-called admitted vectors, and to an interval in the affine symmetric group $\tilde S_n$ with the weak order. The poset is a semidistributive lattice, and the rank function, whose range is cubic in $n$, is computed by some special formula involving inversions. We prove also some links with Eulerian numbers, triangulations of an $n$-gon, and Young's lattice.

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Dates et versions

hal-04677001 , version 1 (28-08-2024)

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Antoine Abram, Nathan Chapelier-Laget, Christophe Reutenauer. An order on circular permutations. The Electronic Journal of Combinatorics, 2021, 28 (3), pp.P3.31. ⟨10.37236/9982⟩. ⟨hal-04677001⟩
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