Graham positivity of triple Schubert calculus

2025/06/11 by Yibo Gao, Rui Xiong, Gao, Yibo +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2506.09421

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Samuel's conjecture on certain Graham positivity of the expansion coefficient of two double Schubert polynomials in three sets of variables by establishing a refined version of Graham's positivity theorem. As a corollary, we prove Kirillov's conjecture on the positivity of skew divided difference operators applied to Schubert polynomials.

Citations

• Bumpless pipe dreams meet Puzzles
• Schubert puzzles and integrability III: separated descents
• Back stable K-theory Schubert calculus
• Back stable Schubert calculus
• Skew divided difference operators in the Nichols algebra associated to a finite Coxeter group
• Positive expressions for skew divided difference operators
• Gröbner geometry of Schubert polynomials
• Positivity in equivariant Schubert calculus
• A Littlewood-Richardson Rule for factorial Schur functions

Related

• Positivity of Schubert Coefficients
• Equivariant Schubert Calculus for Inverse Grassmannian Permutations
• Twisted Schubert polynomials
• A generalization of Edelman--Greene insertion for Schubert polynomials
• Skew divided difference operators and Schubert polynomials