Bumpless pipe dream RSK, growth diagrams, and Schubert structure constants

Daoji Huang; Pavlo Pylyavskyy

Bumpless pipe dream RSK, growth diagrams, and Schubert structure constants

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arxiv 2206.14351 v1 pith:PZSVV5KA submitted 2022-06-29 math.CO

Daoji Huang , Pavlo Pylyavskyy This is my paper · ORCID

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keywords objectsschubertbumplessconstantsdiagramsgrowthinsertionpipe

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We introduce analogs of left and right RSK insertion for Schubert calculus of complete flag varieties. The objects being inserted are certain biwords, the insertion objects are bumpless pipe dreams, and the recording objects are decorated chains in Bruhat order. As an application, we adopt Lenart's growth diagrams of permutations to give a combinatorial rule for Schubert structure constants in the separated descent case.

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Richardson tableaux and Schubert positivity
math.CO 2025-10 conditional novelty 7.0 of 10

The Schubert cycle expansion of a Springer fiber component equal to a Richardson variety, indexed by a Richardson tableau, is computed combinatorially using translation-equivalent Bruhat intervals and Sottile's Pieri rule.

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