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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08609 |
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| _version_ | 1866917692235055104 |
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| author | Cuthbertson, Philip |
| author_facet | Cuthbertson, Philip |
| contents | In a paper by the author, Hemmer, Hopkins, and Keith the concept of a fixed point in a sequence was applied to the sequence of first column hook lengths of a partition. In this paper we generalize this notion to fixed hook lengths in an arbitrary column of a partition. We establish combinatorial connections between these fixed hooks and colored partitions that have interesting gap and mex-like conditions. Additionally, we obtain several generating functions for hook lengths of a given fixedness by hook length or part size in unrestricted partitions as well as some classical restrictions such as odd and distinct partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08609 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed hooks in arbitrary columns Cuthbertson, Philip Combinatorics In a paper by the author, Hemmer, Hopkins, and Keith the concept of a fixed point in a sequence was applied to the sequence of first column hook lengths of a partition. In this paper we generalize this notion to fixed hook lengths in an arbitrary column of a partition. We establish combinatorial connections between these fixed hooks and colored partitions that have interesting gap and mex-like conditions. Additionally, we obtain several generating functions for hook lengths of a given fixedness by hook length or part size in unrestricted partitions as well as some classical restrictions such as odd and distinct partitions. |
| title | Fixed hooks in arbitrary columns |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.08609 |