Schubert polynomials, slide polynomials, Stanley symmetric functions and quasi-Yamanouchi pipe dreams

DOI10.1016/j.aim.2016.10.015zbMath1356.14039arXiv1603.09744OpenAlexW2331950050MaRDI QIDQ728217

Sami Assaf, Dominic Searles

Publication date: 19 December 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09744

zbMATH Keywords

Schubert polynomialsStanley symmetric functionsquasisymmetric functionspipe dreamsreduced decompositions

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items (32)

Demazure crystals for Kohnert polynomials ⋮ Skew key polynomials and a generalized Littlewood-Richardson rule ⋮ Combinatorial bases of polynomials ⋮ Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials ⋮ On the Schur expansion of Jack polynomials ⋮ A Demazure crystal construction for Schubert polynomials ⋮ Kohnert Polynomials ⋮ Weak dual equivalence for polynomials ⋮ Macdonald polynomials and chromatic quasisymmetric functions ⋮ A generalization of the dual immaculate quasisymmetric functions in partially commutative variables ⋮ Kohnert tableaux and a lifting of quasi-Schur functions ⋮ Asymmetric Function Theory ⋮ Polynomials from Combinatorial -theory ⋮ A cornucopia of quasi-Yamanouchi tableaux ⋮ Slide polynomials ⋮ Tableau models for Schubert polynomials ⋮ Flagged \(( \mathcal{P}, \rho)\)-partitions ⋮ A generalization of Edelman-Greene insertion for Schubert polynomials ⋮ Nonsymmetric Macdonald polynomials and a refinement of Kostka–Foulkes polynomials ⋮ Set-valued Rothe tableaux and Grothendieck polynomials ⋮ Demazure crystals for specialized nonsymmetric Macdonald polynomials ⋮ Lifting the dual immaculate functions ⋮ Polynomial bases: Positivity and Schur multiplication ⋮ \(K\)-theoretic polynomials ⋮ Skew polynomials and extended Schur functions ⋮ Skew key polynomials and the key poset ⋮ The genomic Schur function is fundamental-positive ⋮ A weak version of Kirillov's conjecture on Hecke-Grothendieck polynomials ⋮ Slide multiplicity free key polynomials ⋮ The ``Young and ``reverse dichotomy of polynomials ⋮ Slide complexes and subword complexes ⋮ Chromatic nonsymmetric polynomials of Dyck graphs are slide-positive

Cites Work

• On the number of reduced decompositions of elements of Coxeter groups
• Some combinatorial properties of Schubert polynomials
• Schubert polynomials and the nilCoxeter algebra
• Balanced tableaux
• Quasi-shuffle products
• A canonical expansion of the product of two Stanley symmetric functions
• On the groups \(H(\Pi,n)\). I
• RC-Graphs and Schubert Polynomials
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