Séminaire Lotharingien de Combinatoire, 89B.89 (2023), 12 pp.
Allen Knutson and Gabe Udell
Interpolating between Classic and Bumpless Pipe Dreams
Abstract.
We introduce hybrid pipe dreams, in which some rows are
specified to contain classic pipe dream tiles (plus a couple new ones)
and some to contain bumpless pipe dream tiles (albeit upside down).
For each of the 2n possibilities of row specification, there is a sum
over hybrid pipe dreams to compute each double Schubert polynomial.
We give a bijection to swap the specifications
on two adjacent rows, demonstrating the equivalence of the many formulae.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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