Generalizations of Euler's Theorem to $k$-regular partitions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917089496793088 |
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| author | Lin, Hongshu Zang, Wenston J. T. |
| author_facet | Lin, Hongshu Zang, Wenston J. T. |
| contents | Let $A_k(n)$ denote the set of $k$-distinct partitions of $n$, and let $B_k(n)$ be the set of $k$-regular partitions of $n$. Glaisher showed that $\# A_k(n) = \# B_k(n)$. For $k=2$, this equality yields the celebrated Euler's partition theorem. In this paper, we present a new partition set $E_k(n)$, which is equinumerous to $B_k(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizations of Euler's Theorem to $k$-regular partitions Lin, Hongshu Zang, Wenston J. T. Combinatorics Let $A_k(n)$ denote the set of $k$-distinct partitions of $n$, and let $B_k(n)$ be the set of $k$-regular partitions of $n$. Glaisher showed that $\# A_k(n) = \# B_k(n)$. For $k=2$, this equality yields the celebrated Euler's partition theorem. In this paper, we present a new partition set $E_k(n)$, which is equinumerous to $B_k(n)$. |
| title | Generalizations of Euler's Theorem to $k$-regular partitions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.14594 |