Generalizations of Euler's Theorem to $k$-regular partitions

Hongshu Lin; Wenston J. T. Zang

Generalizations of Euler's Theorem to $k$-regular partitions

Combinatorics 2025-11-19 v1

Authors: Hongshu Lin , Wenston J. T. Zang

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 $B_k(n)$ .

Keywords

partition theory partition congruences generalization theorems

Cite

@article{arxiv.2511.14594,
  title  = {Generalizations of Euler's Theorem to $k$-regular partitions},
  author = {Hongshu Lin and Wenston J. T. Zang},
  journal= {arXiv preprint arXiv:2511.14594},
  year   = {2025}
}

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