Séminaire Lotharingien de Combinatoire, 93B.87 (2025), 11 pp.
Philippe Nadeau, Hunter Spink and Vasu Tewari
Quasisymmetric Divided Differences
Abstract.
We develop a quasisymmetric analogue of the combinatorial theory of Schubert polynomials. Indexed binary forests play the role of permutations, and the associated divided difference operators compose according to the "Thompson monoid" governing the Thompson group. Our main application of our theory is to study the ring of quasisymmetric coinvariants and the associated quasisymmetric harmonics spaces. In followup work we describe an algebraic-geometric framework which matches the combinatorial theory.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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