Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916556000198656 |
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| author | Fang, Yaozhou Gao, Xing |
| author_facet | Fang, Yaozhou Gao, Xing |
| contents | For closed $k$-Schur Katalan functions $\fgλ{k}$ with $k$ a positive integer and $λ$ a $k$-bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rule conjecture and the $k$-branching conjecture. In the present paper, we positively prove the first one for large enough $k$ and for strictly decreasing partitions $λ$ respectively, as well as the second one for strictly decreasing partitions $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04200 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions Fang, Yaozhou Gao, Xing Combinatorics 05E05, 05E10, 14N15 For closed $k$-Schur Katalan functions $\fgλ{k}$ with $k$ a positive integer and $λ$ a $k$-bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rule conjecture and the $k$-branching conjecture. In the present paper, we positively prove the first one for large enough $k$ and for strictly decreasing partitions $λ$ respectively, as well as the second one for strictly decreasing partitions $λ$. |
| title | Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions |
| topic | Combinatorics 05E05, 05E10, 14N15 |
| url | https://arxiv.org/abs/2501.04200 |