Abstract:Pipedreams and bumpless pipedreams are two combinatorial models that compute double Grothendieck polynomials. While studying matrix Schubert varieties, Pechenik, Speyer, and Weigandt defined a permutation statistic$\mathsf{rajcode}(\cdot)$ that captures the leading monomial of the top-degree components of a Grothendieck polynomial. Combinatorially, their result implies that there exists a unique pipedream (or 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 bumpless pipedream version of this problem by providing an explicit algorithm.
| Comments: | 10 pages, 20 figures |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05E05, 14N15 |
| Cite as: | arXiv:2605.24511 [math.CO] |
| (or arXiv:2605.24511v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24511 arXiv-issued DOI via DataCite (pending registration) |
From: Sophie Sun [view email]
[v1]
Sat, 23 May 2026 10:52:24 UTC (25 KB)
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