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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.07513 |
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| _version_ | 1866916043563204608 |
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| author | Khanna, Aditya |
| author_facet | Khanna, Aditya |
| contents | The number of standard Young tableaux of shape a partition $λ$ is called the dimension of the partition and is denoted by $f^λ$. Partitions with odd dimensions were enumerated by McKay and were further characterized by Macdonald. Let $a_i(n)$ be the number of partitions of $n$ with dimension congruent to $i$ modulo 4. In this paper, we refine Macdonald's and McKay's results by computing $a_1(n)$ and $a_3(n)$ when $n$ has no consecutive 1s in its binary expansion or when the sum of binary digits of $n$ is 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07513 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Enumeration of Odd-Dimensional Partitions modulo 4 Khanna, Aditya Combinatorics 05E10 (Primary), 20C30 (secondary) The number of standard Young tableaux of shape a partition $λ$ is called the dimension of the partition and is denoted by $f^λ$. Partitions with odd dimensions were enumerated by McKay and were further characterized by Macdonald. Let $a_i(n)$ be the number of partitions of $n$ with dimension congruent to $i$ modulo 4. In this paper, we refine Macdonald's and McKay's results by computing $a_1(n)$ and $a_3(n)$ when $n$ has no consecutive 1s in its binary expansion or when the sum of binary digits of $n$ is 2. |
| title | Enumeration of Odd-Dimensional Partitions modulo 4 |
| topic | Combinatorics 05E10 (Primary), 20C30 (secondary) |
| url | https://arxiv.org/abs/2207.07513 |