Counting Shi Regions with a Fixed Separating Wall

Susanna Fishel, Eleni Tzanaki, Monica Vazirani

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)671-693
Number of pages23
JournalAnnals of Combinatorics
Volume17
Issue number4
DOIs
StatePublished - Nov 2013

Fingerprint

Counting
Hyperplane
Arrangement
Narayana numbers
Facet
Calculate
Generalise

Keywords

  • partitions
  • Shi arrangement

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Counting Shi Regions with a Fixed Separating Wall. / Fishel, Susanna; Tzanaki, Eleni; Vazirani, Monica.

In: Annals of Combinatorics, Vol. 17, No. 4, 11.2013, p. 671-693.

Research output: Contribution to journalArticle

Fishel, Susanna ; Tzanaki, Eleni ; Vazirani, Monica. / Counting Shi Regions with a Fixed Separating Wall. In: Annals of Combinatorics. 2013 ; Vol. 17, No. 4. pp. 671-693.
@article{081de47353b343668d606d43de19139d,
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 = "2013",
month = "11",
doi = "10.1007/s00026-013-0201-x",
language = "English (US)",
volume = "17",
pages = "671--693",
journal = "Annals of Combinatorics",
issn = "0218-0006",
publisher = "Birkhauser Verlag Basel",
number = "4",

}

TY - JOUR

T1 - Counting Shi Regions with a Fixed Separating Wall

AU - Fishel, Susanna

AU - Tzanaki, Eleni

AU - Vazirani, Monica

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 - partitions

KW - Shi arrangement

UR - http://www.scopus.com/inward/record.url?scp=84888297017&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888297017&partnerID=8YFLogxK

U2 - 10.1007/s00026-013-0201-x

DO - 10.1007/s00026-013-0201-x

M3 - Article

VL - 17

SP - 671

EP - 693

JO - Annals of Combinatorics

JF - Annals of Combinatorics

SN - 0218-0006

IS - 4

ER -