中文

Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials

组合数学 2026-05-26 v1

摘要

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 statisticrajcode()\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 rajcode(w)\mathsf{rajcode}(w) and column weight rajcode(w1)\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.

引用

@article{arxiv.2605.24511,
  title  = {Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials},
  author = {Xuanying Han and Sophie C. C. Sun},
  journal= {arXiv preprint arXiv:2605.24511},
  year   = {2026}
}

备注

10 pages, 20 figures