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arXiv · 2303.10463

A pipe dream perspective on totally symmetric self-complementary plane partitions

Daoji Huang·Jessica Striker
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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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Daoji Huang, Jessica Striker. 2023-03-18. A pipe dream perspective on totally symmetric self-complementary plane partitions. https://doi.org/10.1017/fms.2023.131

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