Counting Shi Regions with a Fixed Separating Wall

Susanna Fishel; Eleni Tzanaki; Monica Vazirani

doi:10.1007/s00026-013-0201-x

Counting Shi Regions with a Fixed Separating Wall

Susanna Fishel, Eleni Tzanaki, Monica Vazirani

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	671-693
Number of pages	23
Journal	Annals of Combinatorics
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s00026-013-0201-x
State	Published - Nov 2013

Keywords

Shi arrangement
partitions

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1007/s00026-013-0201-x

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title = "Counting Shi Regions with a Fixed Separating Wall",

abstract = "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.",

keywords = "Shi arrangement, partitions",

author = "Susanna Fishel and Eleni Tzanaki and Monica Vazirani",

note = "Funding Information: ∗Susanna Fishel was partially supported by Simons Foundation Grant 209806. †Monica Vazirani was partially supported by NSA grant H982300910076.",

year = "2013",

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doi = "10.1007/s00026-013-0201-x",

language = "English (US)",

volume = "17",

pages = "671--693",

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T1 - Counting Shi Regions with a Fixed Separating Wall

AU - Fishel, Susanna

AU - Tzanaki, Eleni

AU - Vazirani, Monica

N1 - Funding Information: ∗Susanna Fishel was partially supported by Simons Foundation Grant 209806. †Monica Vazirani was partially supported by NSA grant H982300910076.

PY - 2013/11

Y1 - 2013/11

N2 - 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.

AB - 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.

KW - Shi arrangement

KW - partitions

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U2 - 10.1007/s00026-013-0201-x

DO - 10.1007/s00026-013-0201-x

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AN - SCOPUS:84888297017

SN - 0218-0006

VL - 17

SP - 671

EP - 693

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 4

ER -

Counting Shi Regions with a Fixed Separating Wall

Abstract

Keywords

ASJC Scopus subject areas

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