Residues, Grothendieck polynomials and K-theoretic Thom polynomials

2018/11/05 by Richárd Rimányi, Rimanyi, Richard, András Szenes +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1811.02055

openalex publication_date 2018/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Grothendieck polynomials were introduced by Lascoux and Schützenberger, and they play an important role in K-theoretic Schubert calculus. In this paper, we give a new definition of double stable Grothendieck polynomials based on an iterated residue operation. We illustrate the power of our definition by calculating the Grothendieck expansion of K-theoretic Thom polynomials of A₂ singularities. We present the expansion in two versions: one displays its expected stabilization, while the other displays its expected finiteness property.

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