Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914702917894144 |
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| author | Sha, Yetong Xiong, Huan |
| author_facet | Sha, Yetong Xiong, Huan |
| contents | In 2016, Nath and Sellers proposed a conjecture regarding the precise largest size of ${(s,ms-1,ms+1)}$-core partitions. In this paper, we prove their conjecture. One of the key techniques in our proof is to introduce and study the properties of generalized-$β$-sets, which extend the concept of $β$-sets for core partitions. Our results can be interpreted as a generalization of the well-known result of Yang, Zhong, and Zhou concerning the largest size of $(s,s+1,s+2)$-core partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15899 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions Sha, Yetong Xiong, Huan Combinatorics 05A15, 05A17 In 2016, Nath and Sellers proposed a conjecture regarding the precise largest size of ${(s,ms-1,ms+1)}$-core partitions. In this paper, we prove their conjecture. One of the key techniques in our proof is to introduce and study the properties of generalized-$β$-sets, which extend the concept of $β$-sets for core partitions. Our results can be interpreted as a generalization of the well-known result of Yang, Zhong, and Zhou concerning the largest size of $(s,s+1,s+2)$-core partitions. |
| title | Proof of a Conjecture of Nath and Sellers on Simultaneous Core Partitions |
| topic | Combinatorics 05A15, 05A17 |
| url | https://arxiv.org/abs/2305.15899 |