A bijection between dominant Shi regions and core partitions

Susanna Fishel, Monica Vazirani

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21 Scopus citations

Abstract

It is well-known that Catalan numbers Cn=1n+1(2nn) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n+1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi arrangement and partitions which are both n-cores as well as (mn+1)-cores. The bijection is natural in the sense that it commutes with the action of the affine symmetric group.

Original languageEnglish (US)
Pages (from-to)2087-2101
Number of pages15
JournalEuropean Journal of Combinatorics
Volume31
Issue number8
DOIs
StatePublished - Dec 1 2010

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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