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<p>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.</p>

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Combinatorial interpretations of truncated versions of a identity of Gauss

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Thomas Y. He,
  • S. Y. Liu

摘要

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.