A Description of the Minimal Elements of Shi Regions in Classical Weyl Groups - Laboratoire Interdisciplinaire des Sciences du Numérique Access content directly
Conference Papers Year : 2022

A Description of the Minimal Elements of Shi Regions in Classical Weyl Groups

Abstract

In this extended abstract, we show how a bijection between parking functions and regions of the Shi arrangement from Athanasiadis and Linusson (in type An) and Armstrong, Reiner, and Rhoades (in type Bn, Cn, Dn) 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.
Fichier principal
Vignette du fichier
51.pdf (199.06 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04258739 , version 1 (25-10-2023)

Identifiers

  • HAL Id : hal-04258739 , version 1

Cite

Balthazar Charles. A Description of the Minimal Elements of Shi Regions in Classical Weyl Groups. 34th Conference on Formal Power Series and Algebraic Combinatorics, IISc, Jun 2022, Bangalore, India. ⟨hal-04258739⟩
14 View
0 Download

Share

Gmail Facebook X LinkedIn More