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Pipe dreams and bumpless pipe dreams for vexillary permutations are each known to be in bijection with certain semistandard tableaux via maps due to Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a bijection between the former two sets. In this note we show for vexillary permutations that the Gao-Huang bijection preserves the associated tableaux, giving a new proof of Lenart's result. Our methods extend to give a recording tableau for any bumpless pipe dream.
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A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions
Abstract We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams. Using this characterization and the recent bijection of Gao–Huang between reduced pipe dreams and reduced bumpless pipe dreams, we give a bijection between alternating sign matrices and TSSCPP in the reduced, 1432-avoiding case. We also give a different bijection in the 1432- and 2143-avoiding case that preserves natural poset structures on the associated pipe dreams and bumpless pipe dreams.
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- Award ID(s):
- 2247089
- PAR ID:
- 10512505
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Forum of Mathematics, Sigma
- Volume:
- 12
- ISSN:
- 2050-5094
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/fms.2023.131
