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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ftccsdartic:oai:HAL:hal-01215047v1 2023-05-15T16:50:45+02:00 Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice Kallipoliti, Myrto Kubitzke, Martina 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 Reykjavik, Iceland 2011 https://hal.inria.fr/hal-01215047 https://hal.inria.fr/hal-01215047/document https://hal.inria.fr/hal-01215047/file/dmAO0151.pdf en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS hal-01215047 https://hal.inria.fr/hal-01215047 https://hal.inria.fr/hal-01215047/document https://hal.inria.fr/hal-01215047/file/dmAO0151.pdf info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215047 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.575-586 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] info:eu-repo/semantics/conferenceObject Conference papers 2011 ftccsdartic 2020-12-25T18:15:03Z 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. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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ftccsdartic |
language |
English |
topic |
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] |
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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] Kallipoliti, Myrto Kubitzke, Martina Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
topic_facet |
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] |
description |
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. |
author2 |
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 |
author |
Kallipoliti, Myrto Kubitzke, Martina |
author_facet |
Kallipoliti, Myrto Kubitzke, Martina |
author_sort |
Kallipoliti, Myrto |
title |
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
title_short |
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
title_full |
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
title_fullStr |
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
title_full_unstemmed |
Double homotopy Cohen-Macaulayness for the poset of injective words and the classical NC-partition lattice |
title_sort |
double homotopy cohen-macaulayness for the poset of injective words and the classical nc-partition lattice |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://hal.inria.fr/hal-01215047 https://hal.inria.fr/hal-01215047/document https://hal.inria.fr/hal-01215047/file/dmAO0151.pdf |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215047 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.575-586 |
op_relation |
hal-01215047 https://hal.inria.fr/hal-01215047 https://hal.inria.fr/hal-01215047/document https://hal.inria.fr/hal-01215047/file/dmAO0151.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766040873592684544 |