Counting Shi Regions with a Fixed Separating Wall

Susanna Fishel, Eleni Tzanaki, Monica Vazirani

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)671-693
Number of pages23
JournalAnnals of Combinatorics
Volume17
Issue number4
DOIs
StatePublished - Nov 1 2013

Keywords

  • Shi arrangement
  • partitions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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