AI 中文总结
该研究受相关组合方法启发，对\(l\)-正则划分及其变体的三个恒等式给出组合证明，其中两个恒等式此前由他人通过解析方法建立，此为恒等式证明提供了新的组合证明方式。
AI 中文摘要
已知按部分数奇偶性对\(l\)-正则划分进行带符号枚举对应于具有同余条件的划分。受Ballantine - Merca和Liu近期此类恒等式组合方法的启发，我们给出了\(l\)-正则划分及其变体的三个恒等式的组合证明。其中两个最初分别由Hickerson和Robbins通过解析方法建立。
英文摘要
Signed enumerations of l-regular partitions by the parity of the number of parts are known to correspond to partitions with congruence conditions. Inspired by the recent combinatorial approaches of Ballantine-Merca and Liu for such identities, we provide combinatorial proofs of three identities for l-regular partitions and their variants. Two of these were originally established analytically by Hickerson and Robbins, respectively.
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