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arXiv · 2605.24511

Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials

Xuanying Han·Sophie C. C. Sun
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Abstract

Pipedreams and bumpless pipedreams are two combinatorial models that compute double Grothendieck polynomials. While studying matrix Schubert varieties, Pechen Pipedreams and marked bumpless pipedreams are two combinatorial models that compute double Grothendieck polynomials. While studying matrix Schubert varieties, Pechenik, Speyer, and Weigandt defined the Rajchgot code, denoted by $\mathsf{rajcode}(\cdot)$, which captures the leading monomial of the top-degree component of a Grothendieck polynomial. Combinatorially, their result implies that there exists a unique pipedream (or marked bumpless pipedream) with row weight $\mathsf{rajcode}(w)$ and column weight $\mathsf{rajcode}(w^{-1})$. A construction of such a pipedream was subsequently given by Chou and Yu. In this paper, we resolve the marked bumpless pipedream version of this problem by providing an explicit algorithm.

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Xuanying Han, Sophie C. C. Sun. 2026-05-23. Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials. https://arxiv.org/abs/2605.24511

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