Article Dans Une Revue Order Année : 2025

The interval posets of permutations seen from the decomposition tree perspective

Résumé

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.

Fichier principal
Vignette du fichier
2110.10000v5.pdf (529.76 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-03456772 , version 1 (04-05-2026)

Licence

Identifiants

Citer

Mathilde Bouvel, Lapo Cioni, Benjamin Izart. The interval posets of permutations seen from the decomposition tree perspective. Order, 2025, 42, pp.459-479. ⟨10.1007/s11083-024-09690-w⟩. ⟨hal-03456772⟩
261 Consultations
0 Téléchargements

Altmetric

Partager

  • More