Year: 2024
Type: preprint
Abstract: We extend the bijection of Fishel-Vazirani on dominant regions of the $m$-Shi arrangement. Our map puts the set of all minimal chambers of the $m$-Shi arrangement of Type $A_{n}$ in bijection with a certain set of (equivalence classes of) $n$-core partitions. As a step to our proof, we give a potentially interesting classification of the alcoves in the $S_{n}$-orbit of an $m$-minimal alcove which are themselves $m$-minimal.
Source: arXiv (Cornell University)
Author: Davis, Matthew
Institution: Muskingum University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403786528