A description of the minimal elements of Shi regions in classical Weyl Groups

Balthazar Charles

A description of the minimal elements of Shi regions in classical Weyl Groups

Combinatorics 2022-01-26 v1 Group Theory

Authors: Balthazar Charles

Abstract

In this extended abstract, we show how a bijection between parking functions and regions of the Shi arrangement from [Athanasiadis, Linusson '99] (in type $A_n$ ) and [Armstrong, Reiner, Rhoades '15] (in type $B_n, C_n, D_n$ ) allows for the computation of the minimal elements of the Shi regions. This gives a combinatorial interpretation of these minimal elements: they can be seen as counting non-crossing arcs in non-nesting arc diagrams.

Keywords

Shi arrangement Weyl groups parking functions minimal elements combinatorial interpretation non-crossing arcs

Cite

@article{arxiv.2201.10233,
  title  = {A description of the minimal elements of Shi regions in classical Weyl Groups},
  author = {Balthazar Charles},
  journal= {arXiv preprint arXiv:2201.10233},
  year   = {2022}
}

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12 pages, 3 figures, 4 tables

A description of the minimal elements of Shi regions in classical Weyl Groups

Abstract

Keywords

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