Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice

International audience In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extend...

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Bibliographic Details
Main Authors: Kallipoliti, Myrto, Kubitzke, Martina
Other Authors: Department of Mathematics Athens, National and Kapodistrian University of Athens (NKUA), Erwin Schrödinger Institute for Mathematical Physics, ESIMP, Fakultät für Mathematik Wien, Universität Wien, Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
Format: Conference Object
Language:English
Published: HAL CCSD 2011
Subjects:
injective words
non-crossing partitions
strongly constructible
doubly homotopy Cohen-Macaulay
poset fiber theorem
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Iceland
Online Access:https://hal.inria.fr/hal-01215047
https://hal.inria.fr/hal-01215047/document
https://hal.inria.fr/hal-01215047/file/dmAO0151.pdf
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Summary:International audience In this paper we study topological properties of the poset of injective words and the lattice of classical non-crossing partitions. Specifically, it is shown that after the removal of the bottom and top elements (if existent) these posets are doubly Cohen-Macaulay. This extends the well-known result that those posets are shellable. Both results rely on a new poset fiber theorem, for doubly homotopy Cohen-Macaulay posets, which can be considered as an extension of the classical poset fiber theorem for homotopy Cohen-Macaulay posets. Dans cet article, nous étudions certaines propriétés topologiques du poset des mots injectifs et du treillis des partitions non-croisées classiques. Plus précisément, nous montrons qu'après suppression des plus petit et plus grand élément (s'ils existent), ces posets sont doublement Cohen-Macaulay. C'est une extension du fait bien connu que ces deux posets sont épluchables ("shellable''). Ces deux résultats reposent sur un nouveau théorème poset-fibre pour les posets doublement homotopiquement Cohen-Macaulay, que l'on peut voir comme extension du théorème poset-fibre classique pour les posets homotopiquement Cohen-Macaulay.

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