Combinatorial properties of three classical truncated theta series theorems (Q6542435)

George E. Andrews and the reviewer have collaborated on various research projects, combining their expertise to solve complex problems and uncover new mathematical truths. Their joint efforts have resulted in important findings, particularly in the areas of truncated series, enhancing the understanding of these mathematical concepts [\textit{G. E. Andrews} and \textit{M. Merca}, J. Comb. Theory, Ser. A 119, No. 8, 1639--1643 (2012; Zbl 1246.05014); J. Comb. Theory, Ser. A 154, 610--619 (2018; Zbl 1454.05015)]. \N\NThe main purpose of this paper is to explore the potential combinatorial structures behind the truncations of three classical theta series of Euler and Gauss, and provide combinatorial proofs of some truncated theta identities in a unified manner.