A visual approach to symmetric chain decompositions of finite Young lattices
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910545665327104 |
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| author | Coggins, Terrance Donley Jr., Robert W. Gondal, Ammara Krishna, Arnav |
| author_facet | Coggins, Terrance Donley Jr., Robert W. Gondal, Ammara Krishna, Arnav |
| contents | The finite Young lattice $L(m, n)$ is rank-symmetric, rank-unimodal, and has the strong Sperner property. R. Stanley further conjectured that $L(m, n)$ admits a symmetric chain order. We show that the order structure on $L(m, n)$ is equivalent to a natural ordering on the lattice points of a dilated $n$-simplex, which in turn corresponds to a weight diagram for the root system of type $A_n$. Lindstr{\" o}m's symmetric chain decompositions for $L(3, n)$ are described completely through pictures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20008 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A visual approach to symmetric chain decompositions of finite Young lattices Coggins, Terrance Donley Jr., Robert W. Gondal, Ammara Krishna, Arnav Combinatorics 05A17 06A07 The finite Young lattice $L(m, n)$ is rank-symmetric, rank-unimodal, and has the strong Sperner property. R. Stanley further conjectured that $L(m, n)$ admits a symmetric chain order. We show that the order structure on $L(m, n)$ is equivalent to a natural ordering on the lattice points of a dilated $n$-simplex, which in turn corresponds to a weight diagram for the root system of type $A_n$. Lindstr{\" o}m's symmetric chain decompositions for $L(3, n)$ are described completely through pictures. |
| title | A visual approach to symmetric chain decompositions of finite Young lattices |
| topic | Combinatorics 05A17 06A07 |
| url | https://arxiv.org/abs/2407.20008 |