Stack-Sorting for Coxeter Groups
Colin Defant

TL;DR
This paper generalizes the concept of stack-sorting operators to Coxeter groups, establishing new bounds and analogues of classical results, including type-B and affine types, with applications to permutation sorting.
Contribution
It introduces Coxeter stack-sorting operators based on lattice congruences, extending known sorting maps to broader Coxeter group contexts, and develops analogues for types B and affine A.
Findings
Permutations in the image have at most (2(n-1)/3) ight floor right descents.
Bound on right descents is tight.
Analogues of classical sorting results are established for new operators.
Abstract
Given an essential semilattice congruence on the left weak order of a Coxeter group , we define the Coxeter stack-sorting operator by , where is the unique minimal element of the congruence class of containing . When is the sylvester congruence on the symmetric group , the operator is West's stack-sorting map. When is the descent congruence on , the operator is the pop-stack-sorting map. We establish several general results about Coxeter stack-sorting operators, especially those acting on symmetric groups. For example, we prove that if is an essential lattice congruence on , then every permutation in the image of has at most…
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · semigroups and automata theory
