Double Schubert polynomials do have saturated Newton polytopes

2021/09/21 by Federico Castillo, Castillo, Federico, Yairon Cid‐Ruiz +5 · 3 citations
Mathematics · #13H15 #14C17 #14M15 #52B40 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2109.10299

openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study non-standard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen-Macaulay prime ideal, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid.

Cited by

• Saturation for Non-Symmetric Macdonald Polynomials
• Supersymmetric Schur polynomials have saturated Newton polytopes
• Hybrid Grothendieck polynomials

Related

• Newton polytopes of dual Schubert polynomials
• Schubert polynomials and patterns in permutations
• Newton polytopes of fireworks Grothendieck polynomials
• Saturation for Non-Symmetric Macdonald Polynomials
• Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes