Postnikov--Stanley polynomials are Lorentzian

2024/12/03 by Serena An, An, Serena, Katherine Tung +3 · 2 citations
Engineering · Computer Science · Mathematics · #Advanced Numerical Analysis Techniques #Polynomial and algebraic computation #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2412.02051

Abstract

Postnikov--Stanley polynomials D_u^w are a generalization of skew dual Schubert polynomials to the setting of arbitrary Weyl groups. We prove that Postnikov--Stanley polynomials are Lorentzian by showing that they are degree polynomials of Richardson varieties. Our result yields an interesting class of Lorentzian polynomials related to the geometry of Richardson varieties, generalizes the result that dual Schubert polynomials are Lorentzian (Huh--Matherne--Mészáros--St. Dizier 2022), and resolves the conjecture that Postnikov--Stanley polynomials have M-convex support (An--Tung--Zhang 2024).

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Related

• Lorentzian polynomials
• K-Lorentzian Polynomials
• Stanley symmetric functions and quiver varieties
• Billey-Postnikov posets, rationally smooth Schubert varieties, and Poincaré duality
• Symmetric Lorentzian Polynomials