Geodesic
Labeling the regions of the type \(C_n\) Shi arrangement
Karola Mészáros1
1Cornell University
The electronic journal of combinatorics, Tome 20 (2013) no. 2
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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.
DOI : 10.37236/3272
Classification : 52C35, 06A07
Mots-clés : type \(C_n\) Shi arrangements, sequences, posets, nonnesting partitions

Karola Mészáros  1

1 Cornell University 
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     title = {Labeling the regions of the type {\(C_n\)} {Shi} arrangement},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {2},
     doi = {10.37236/3272},
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Karola Mészáros. Labeling the regions of the type \(C_n\) Shi arrangement. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3272

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