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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.11977 |
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| _version_ | 1866909903791063040 |
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| author | Khanna, Aditya |
| author_facet | Khanna, Aditya |
| contents | The number of standard Young tableaux possible of shape corresponding to 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 using the theory of 2-core towers. We use the same theory to extend the results to partitions of $n$ with dimensions congruent to 2 modulo 4 which are enumerated by $a_2(n)$. We provide explicit results for $a_2(n)$ when $n$ has no consecutive 1s in its binary expansion and give a recursive formula to compute $a_2(n)$ for all $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of Even Dimensional Partitions modulo 4 Khanna, Aditya Combinatorics 05A17 (primary), 20C30 (secondary) The number of standard Young tableaux possible of shape corresponding to 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 using the theory of 2-core towers. We use the same theory to extend the results to partitions of $n$ with dimensions congruent to 2 modulo 4 which are enumerated by $a_2(n)$. We provide explicit results for $a_2(n)$ when $n$ has no consecutive 1s in its binary expansion and give a recursive formula to compute $a_2(n)$ for all $n$. |
| title | Enumeration of Even Dimensional Partitions modulo 4 |
| topic | Combinatorics 05A17 (primary), 20C30 (secondary) |
| url | https://arxiv.org/abs/2511.11977 |