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

Balthazar Charles (1)

1 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique

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.

Domaines: Combinatoire [math.CO]

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⟩