Counting Shi regions with a fixed separating wall
International audience Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fix...
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ftccsdartic:oai:HAL:hal-01215106v1 2023-05-15T16:49:56+02:00 Counting Shi regions with a fixed separating wall Fishel, Susanna Tzanaki, Eleni Vazirani, Monica School of Mathematical and Statistical Sciences (Arizona, Tempe) Arizona State University Tempe (ASU) Department of Applied Mathematics Heraklion University of Crete Heraklion (UOC) Department of Mathematics Davis University of California Davis (UC Davis) University of California-University of California Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel Reykjavik, Iceland 2011 https://hal.inria.fr/hal-01215106 https://hal.inria.fr/hal-01215106/document https://hal.inria.fr/hal-01215106/file/dmAO0132.pdf en eng HAL CCSD Discrete Mathematics and Theoretical Computer Science DMTCS hal-01215106 https://hal.inria.fr/hal-01215106 https://hal.inria.fr/hal-01215106/document https://hal.inria.fr/hal-01215106/file/dmAO0132.pdf info:eu-repo/semantics/OpenAccess ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science (DMTCS) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215106 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.351-362 Shi arrangement partitions [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 Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin. Athanasiadis a introduit la notion d'hyperplan de séparation pour une région dans l'arrangement de Shi et l'a utilisée pour généraliser les numéros de Narayana. Dans cet article, nous fixons un hyperplan dans l'arrangement de Shi pour le type A et calculons le nombre de régions dominantes qui ont l'hyperplan fixe pour mur de séparation, c'est-à-dire les régions où l'hyperplan soutient une facette de la région et sépare la région de l'origine. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
institution |
Open Polar |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
Shi arrangement partitions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
spellingShingle |
Shi arrangement partitions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] Fishel, Susanna Tzanaki, Eleni Vazirani, Monica Counting Shi regions with a fixed separating wall |
topic_facet |
Shi arrangement partitions [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] |
description |
International audience Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin. Athanasiadis a introduit la notion d'hyperplan de séparation pour une région dans l'arrangement de Shi et l'a utilisée pour généraliser les numéros de Narayana. Dans cet article, nous fixons un hyperplan dans l'arrangement de Shi pour le type A et calculons le nombre de régions dominantes qui ont l'hyperplan fixe pour mur de séparation, c'est-à-dire les régions où l'hyperplan soutient une facette de la région et sépare la région de l'origine. |
author2 |
School of Mathematical and Statistical Sciences (Arizona, Tempe) Arizona State University Tempe (ASU) Department of Applied Mathematics Heraklion University of Crete Heraklion (UOC) Department of Mathematics Davis University of California Davis (UC Davis) University of California-University of California Bousquet-Mélou Mireille and Wachs Michelle and Hultman Axel |
format |
Conference Object |
author |
Fishel, Susanna Tzanaki, Eleni Vazirani, Monica |
author_facet |
Fishel, Susanna Tzanaki, Eleni Vazirani, Monica |
author_sort |
Fishel, Susanna |
title |
Counting Shi regions with a fixed separating wall |
title_short |
Counting Shi regions with a fixed separating wall |
title_full |
Counting Shi regions with a fixed separating wall |
title_fullStr |
Counting Shi regions with a fixed separating wall |
title_full_unstemmed |
Counting Shi regions with a fixed separating wall |
title_sort |
counting shi regions with a fixed separating wall |
publisher |
HAL CCSD |
publishDate |
2011 |
url |
https://hal.inria.fr/hal-01215106 https://hal.inria.fr/hal-01215106/document https://hal.inria.fr/hal-01215106/file/dmAO0132.pdf |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
ISSN: 1462-7264 EISSN: 1365-8050 Discrete Mathematics and Theoretical Computer Science Discrete Mathematics and Theoretical Computer Science (DMTCS) 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) https://hal.inria.fr/hal-01215106 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.351-362 |
op_relation |
hal-01215106 https://hal.inria.fr/hal-01215106 https://hal.inria.fr/hal-01215106/document https://hal.inria.fr/hal-01215106/file/dmAO0132.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766040104923561984 |