Séminaire Lotharingien de Combinatoire, 95B.89 (2026), 12 pp.
Jack Chen-An Chou, Linus Setiabrata and Tianyi Yu
Grothendieck Polynomials of Fireworks and Inverse Fireworks Permutations
Abstract.
Grothendieck polynomials were introduced by Lascoux and Schützenberger
to represent K-classes of structure sheaves of Schubert varieties.
Their supports and top-degree components have recently become active areas of research. Using pipe dreams, combinatorial objects that compute Grothendieck polynomials, we prove several results for the Grothendieck polynomials of two families of permutations. For fireworks permutations, we show that the support of the Grothendieck polynomial is "as large as possible" and is M-convex after homogenization. For inverse fireworks permutations, we show that every monomial of non-maximal degree appearing in the Grothendieck polynomial divides another monomial of degree exactly one higher. Our work also yields the first direct combinatorial formula for the top-degree components of Grothendieck polynomials.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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