Symmetric quasisymmetric Schur-like functions

2025/07/10 by Esipova, Maria, Liang, Jinting, van Willigenburg, Stephanie
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.08083

Abstract

In this paper we classify when (row-strict) dual immaculate functions and (row-strict) extended Schur functions, as well as their skew generalizations, are symmetric. We also classify when their natural variants, termed advanced functions, are symmetric. In every case our classification recovers classical skew Schur functions.

Citations

• When is the chromatic quasisymmetric function symmetric?
• The skew immaculate Hecke poset and 0-Hecke modules
• Row-strict dual immaculate functions
• 0-Hecke modules for row-strict dual immaculate functions
• Schur functions in noncommuting variables
• Kohnert polynomials
• Set-Valued Skyline Fillings
• Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions
• A proof of the shuffle conjecture
• Row-strict quasisymmetric Schur functions
• QSym over Sym has a stable basis

Related

• Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions
• From symmetric fundamental expansions to Schur positivity
• Row-strict quasisymmetric Schur functions
• A note on passing from a quasi-symmetric function expansion to a Schur\n function expansion of a symmetric function
• Doubly Symmetric Functions