A bijection between $321$- and $213$-avoiding permutations preserving $t$-stack-sortability
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912478609276928 |
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| author | Li, Yang Kitaev, Sergey Lin, Zhicong Liu, Jing |
| author_facet | Li, Yang Kitaev, Sergey Lin, Zhicong Liu, Jing |
| contents | We construct a bijection between $321$- and $213$-avoiding permutations that preserves the property of $t$-stack-sortability. Our bijection transforms natural statistics between these two classes of permutations and proves a refinement of an enumerative conjecture posed by Zhang and Kitaev. This work contributes further to the long-standing line of research on bijections between length-3 pattern avoiding permutations. Increasing binary trees lie at the heart of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A bijection between $321$- and $213$-avoiding permutations preserving $t$-stack-sortability Li, Yang Kitaev, Sergey Lin, Zhicong Liu, Jing Combinatorics We construct a bijection between $321$- and $213$-avoiding permutations that preserves the property of $t$-stack-sortability. Our bijection transforms natural statistics between these two classes of permutations and proves a refinement of an enumerative conjecture posed by Zhang and Kitaev. This work contributes further to the long-standing line of research on bijections between length-3 pattern avoiding permutations. Increasing binary trees lie at the heart of our approach. |
| title | A bijection between $321$- and $213$-avoiding permutations preserving $t$-stack-sortability |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.09187 |