Combinatorial interpretation of a truncated identity of Gauss

2025/09/01 by Thomas Y. He, He, Thomas Y., Shilong Liu +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2509.01216

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.

Citations

• Combinatorial Proof of the Minimal Excludant Theorem
• Partitions and the Minimal Excludant

Related

• Partition-theoretic interpretation for certain truncated series
• Truncated theta series from the Bailey lattice
• Some truncated identities of Gauss
• Truncated Theta Series Related to the Jacobi Triple Product Identity
• Truncated Series with Nonnegative Coefficients from the Jacobi Triple Product