Séminaire Lotharingien de Combinatoire, 86B.51 (2022), 12 pp.

Balthazar Charles

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 A_n) and Armstrong, Reiner, and Rhoades (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.

Received: November 25, 2021. Accepted: March 4, 2022. Final version: April 1, 2022.

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