Séminaire Lotharingien de Combinatoire, 91B.93 (2024), 12 pp.
Tianyi Yu
Analogues of Two Classical Pipedream Results on Bumpless Pipedreams
Abstract.
Schubert polynomials are distinguished representatives of Schubert cycles in the cohomology of the flag variety. Pipedreams (PD) and bumpless pipedreams (BPD) are two combinatorial models of Schubert polynomials. There are many classical results on PDs. For instance, Fomin and Stanley represented each PD as an element in the nil-Coexter algebra. Lenart and Sottile converted each PD into certain chains in the Bruhat order. This paper establishes the BPD analogues of both viewpoints. Our
results lead to a bijection between PDs and BPDs via Lenart's growth diagram.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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