Proof of a Conjecture on Young Tableaux with Walls
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915732235747328 |
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| author | Lin, Zhicong Liu, Feihu Liu, Jiahang Liu, Jing Xin, Guoce |
| author_facet | Lin, Zhicong Liu, Feihu Liu, Jiahang Liu, Jing Xin, Guoce |
| contents | Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by Chang, Fuchs, Liu, Wallner, and Yu leads to the verification of a conjecture on tree-child networks proposed by Pons and Batle. This conjecture was regarded as a specific and challenging problem in the Phylogenetics community until it was finally resolved by the present work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09551 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof of a Conjecture on Young Tableaux with Walls Lin, Zhicong Liu, Feihu Liu, Jiahang Liu, Jing Xin, Guoce Combinatorics Banderier, Marchal, and Wallner considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. In this work, we prove a conjecture of Fuchs and Yu concerning the enumeration of two classes of three-row Young tableaux with walls. Combining with the work by Chang, Fuchs, Liu, Wallner, and Yu leads to the verification of a conjecture on tree-child networks proposed by Pons and Batle. This conjecture was regarded as a specific and challenging problem in the Phylogenetics community until it was finally resolved by the present work. |
| title | Proof of a Conjecture on Young Tableaux with Walls |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.09551 |