Labeling the regions of the type \(C_n\) Shi arrangement
type: Item
instance of: scholarly article
title: Labeling the regions of the type \(C_n\) Shi arrangement
zbMATH Open document ID: 1270.52029
author: Karola Mészáros
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v20i2p31
review text: Summary: The number of regions of the type \(C_n\) Shi arrangement in \(\mathbb{R}^n\) is \((2n+1)^n\). Strikingly, no bijective proof of this fact has been given thus far. The aim of this paper is to provide such a bijection and use it to prove more refined results. We construct a bijection between the regions of the type \(C_n\) Shi arrangement in \(\mathbb{R}^n\) and sequences \(a_1a_2 \ldots a_n\), where \(a_i \in \{-n, -n+1, \ldots, -1, 0, 1, \ldots, n-1, n\}, i \in [n]\). Our bijection naturally restrict to bijections between special regions of the arrangement and sequences with a given number of distinct elements.
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 6171946
zbMATH Keywords: type \(C_n\) Shi arrangements
zbMATH Keywords: sequences
zbMATH Keywords: posets
zbMATH Keywords: nonnesting partitions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6171946