Counting Shi regions with a fixed separating wall

Susanna Fishel; Eleni Tzanaki; Monica Vazirani

Counting Shi regions with a fixed separating wall

Susanna Fishel
, Eleni Tzanaki
, Monica Vazirani

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 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)
Title of host publication	FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics
Pages	351-362
Number of pages	12
State	Published - 2011
Event	23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 - Reykjavik, Iceland Duration: Jun 13 2011 → Jun 17 2011

Other

Other	23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11
Country/Territory	Iceland
City	Reykjavik
Period	6/13/11 → 6/17/11

Keywords

Partitions
Shi arrangement

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

@inproceedings{7680931d4bb54386ac9f370f2e88b4ca,

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 = "Partitions, Shi arrangement",

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

year = "2011",

language = "English (US)",

pages = "351--362",

booktitle = "FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics",

note = "23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 ; Conference date: 13-06-2011 Through 17-06-2011",

}

TY - GEN

T1 - Counting Shi regions with a fixed separating wall

AU - Fishel, Susanna

AU - Tzanaki, Eleni

AU - Vazirani, Monica

PY - 2011

Y1 - 2011

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 - Partitions

KW - Shi arrangement

UR - https://www.scopus.com/pages/publications/84860466202

UR - https://www.scopus.com/pages/publications/84860466202#tab=citedBy

M3 - Conference contribution

AN - SCOPUS:84860466202

SP - 351

EP - 362

BT - FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics

T2 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11

Y2 - 13 June 2011 through 17 June 2011

ER -

Counting Shi regions with a fixed separating wall

Abstract

Other

Keywords

ASJC Scopus subject areas

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