Coxeter Pop-Tsack Torsing
Colin Defant, Nathan Williams

TL;DR
This paper introduces a new operator on finite Coxeter groups, generalizing pop-stack sorting, and analyzes its periodic points and orbits, revealing connections to Coxeter group types and the Coxeter number.
Contribution
It defines the Coxeter pop-tsack torsing operator and characterizes its dynamics, including periodic points and orbit sizes, for various Coxeter group types, extending previous sorting map concepts.
Findings
Identity is the unique periodic point for certain types.
Maximum orbit size equals the Coxeter number h.
Coincidental type groups have a unique orbit of size h.
Abstract
Given a finite irreducible Coxeter group with a fixed Coxeter element , we define the Coxeter pop-tsack torsing operator by , where is the join in the noncrossing partition lattice of the set of reflections lying weakly below in the absolute order. This definition serves as a "Bessis dual" version of the first author's notion of a Coxeter pop-stack sorting operator, which, in turn, generalizes the pop-stack-sorting map on symmetric groups. We show that if is coincidental or of type , then the identity element of is the unique periodic point of and the maximum size of a forward orbit of is the Coxeter number of . In each of these types, we obtain a natural lift from to the dual braid monoid of . We also prove that is…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · semigroups and automata theory
