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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Bibliographic Details
Main Authors: Fishel, Susanna, Tzanaki, Eleni, Vazirani, Monica
Other Authors: 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
Language:English
Published: HAL CCSD 2011
Subjects:
Shi arrangement
partitions
[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-01215106
https://hal.inria.fr/hal-01215106/document
https://hal.inria.fr/hal-01215106/file/dmAO0132.pdf
Description
Summary: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.

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