A pipe dream perspective on totally symmetric self-complementary plane partitions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916113551458304 |
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| author | Huang, Daoji Striker, Jessica |
| author_facet | Huang, Daoji Striker, Jessica |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10463 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A pipe dream perspective on totally symmetric self-complementary plane partitions Huang, Daoji Striker, Jessica Combinatorics 05A19 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. |
| title | A pipe dream perspective on totally symmetric self-complementary plane partitions |
| topic | Combinatorics 05A19 |
| url | https://arxiv.org/abs/2303.10463 |