Quasisymmetric divided differences
Abstract
We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials and the associated divided difference operators. Our counterparts are "forest polynomials", and a new family of linear operators, whose theory of compositions is governed by forests and the "Thompson monoid". Our approach extends naturally to -colored quasisymmetric functions. We then give several applications of our theory to fundamental quasisymmetric functions, the study of quasisymmetric coinvariant rings and their associated harmonics, and positivity results for various expansions. In particular we resolve a conjecture of Aval-Bergeron-Li regarding quasisymmetric harmonics.
Cite
@article{arxiv.2406.01510,
title = {Quasisymmetric divided differences},
author = {Philippe Nadeau and Hunter Spink and Vasu Tewari},
journal= {arXiv preprint arXiv:2406.01510},
year = {2026}
}
Comments
57 pages; the general $m$-quasisymmetric setup now is one appendix and the main body is the usual quasisymmetric case