Bijective proof of a conjecture on unit interval posets
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916139510005760 |
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| author | Fang, Wenjie |
| author_facet | Fang, Wenjie |
| contents | In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently by Gélinas, Segovia and Thomas using induction. In this short note, we provide a bijective proof of the same conjecture with a reformulation of the zeta map using left-aligned colored trees, first proposed in the study of parabolic Tamari lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13040 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bijective proof of a conjecture on unit interval posets Fang, Wenjie Combinatorics In a recent preprint, Matherne, Morales and Selover conjectured that two different representations of unit interval posets are related by the famous zeta map in $q,t$-Catalan combinatorics. This conjecture was proved recently by Gélinas, Segovia and Thomas using induction. In this short note, we provide a bijective proof of the same conjecture with a reformulation of the zeta map using left-aligned colored trees, first proposed in the study of parabolic Tamari lattices. |
| title | Bijective proof of a conjecture on unit interval posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2212.13040 |