Year: 2025
Type: preprint
Abstract: 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 $B_k(n)$.
Source: arXiv (Cornell University)
Authors: Lin, Hongshu, Zang, Wenston J. T.
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106102206
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