On linear intervals in the alt $ν$-Tamari lattices
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912327025033216 |
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| author | Ceballos, Cesar Chenevière, Clément |
| author_facet | Ceballos, Cesar Chenevière, Clément |
| contents | Given a lattice path $ν$, the $ν$-Tamari lattice and the $ν$-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above $ν$. In this paper, we introduce a more general family of lattices, called alt $ν$-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02250 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On linear intervals in the alt $ν$-Tamari lattices Ceballos, Cesar Chenevière, Clément Combinatorics 06A07, 06B05, 05A19 Given a lattice path $ν$, the $ν$-Tamari lattice and the $ν$-Dyck lattice are two natural examples of partial order structures on the set of lattice paths that lie weakly above $ν$. In this paper, we introduce a more general family of lattices, called alt $ν$-Tamari lattices, which contains these two examples as particular cases. Unexpectedly, we show that all these lattices have the same number of linear intervals. |
| title | On linear intervals in the alt $ν$-Tamari lattices |
| topic | Combinatorics 06A07, 06B05, 05A19 |
| url | https://arxiv.org/abs/2305.02250 |