English

Combinatorial interpretation of a truncated identity of Gauss

Combinatorics 2025-09-25 v3

Abstract

In 2012, Andrews and Merca proved a truncated theorem on Euler's pentagonal number theorem, which opened up a new study on truncated theta series. In particular, some truncated versions of a identity of Gauss have been proved. In this article, we provide new combinatorial interpretations of the truncated versions of the identity of Gauss in terms of the minimal excludant non-overlined part of an overpartition.

Keywords

Cite

@article{arxiv.2509.01216,
  title  = {Combinatorial interpretation of a truncated identity of Gauss},
  author = {Thomas Y. He and S. Y. Liu},
  journal= {arXiv preprint arXiv:2509.01216},
  year   = {2025}
}