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Marked Bumpless Pipedreams and Compatible Pairs

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arxiv 2407.18160 v1 pith:EFWYRO45 submitted 2024-07-25 math.CO

Daoji Huang , Mark Shimozono , Tianyi Yu This is my paper · ORCID
classification math.CO
keywords bijectionpipedreamsbumplesscompatiblemarkedpairscaseconstruct
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We construct a bijection between marked bumpless pipedreams with reverse compatible pairs, which are in bijection with not-necessarily-reduced pipedreams. This directly unifies various formulas for Grothendieck polynomials in the literature. Our bijection is a generalization of a variant of the bijection of Gao and Huang in the unmarked, reduced case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Changing Bases with Pipe Dream Combinatorics

    math.CO 2025-06 conditional novelty 6.0 of 10

    New combinatorial formulas, via bumpless pipe dreams and pipe dreams, express Grothendieck polynomials in the Schubert basis and Schubert polynomials in the Grothendieck basis, and extend to the back stable setting.

  2. Introduction to the Cohomology of the Flag Variety

    math.CO 2025-06 unverdicted novelty 2.0 of 10

    A survey chapter presenting the cohomology of flag varieties and Schubert and Schur polynomials as the rigorous basis for solving Schubert's enumerative geometry problems.

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