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<p>The <i>K</i>-theoretic quiver component formula expresses the <i>K</i>-polynomial of a type <i>A</i> quiver locus as an alternating sum of products of double Grothendieck polynomials. This formula was conjectured by A. Buch and R. Rimányi and later proved by R. Kinser, A. Knutson, and the second author. We provide a new proof of this formula which replaces Gröbner degenerations by combinatorics. Along the way, we obtain a new proof of A. Buch and R. Rimányi’s cohomological quiver component formula. Again, our proof replaces geometric techniques by combinatorics.</p>

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Combinatorial proofs of the type A quiver component formulas

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Aidan Lindberg,
  • Jenna Rajchgot

摘要

The K-theoretic quiver component formula expresses the K-polynomial of a type A quiver locus as an alternating sum of products of double Grothendieck polynomials. This formula was conjectured by A. Buch and R. Rimányi and later proved by R. Kinser, A. Knutson, and the second author. We provide a new proof of this formula which replaces Gröbner degenerations by combinatorics. Along the way, we obtain a new proof of A. Buch and R. Rimányi’s cohomological quiver component formula. Again, our proof replaces geometric techniques by combinatorics.