Counting Shi regions with a fixed separating wall

Susanna Fishel, Eleni Tzanaki, Monica Vazirani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 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)
Title of host publicationFPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics
Pages351-362
Number of pages12
StatePublished - 2011
Event23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11 - Reykjavik, Iceland
Duration: Jun 13 2011Jun 17 2011

Other

Other23rd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'11
CountryIceland
CityReykjavik
Period6/13/116/17/11

Keywords

  • Partitions
  • Shi arrangement

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Fishel, S., Tzanaki, E., & Vazirani, M. (2011). Counting Shi regions with a fixed separating wall. In FPSAC'11 - 23rd International Conference on Formal Power Series and Algebraic Combinatorics (pp. 351-362)