论文标题
Modulo $ d $平价扩展导致Rogers-Ramanujan-Gordon类型的分区身份
Modulo $d$ extension of parity results in Rogers-Ramanujan-Gordon type overpartition identities
论文作者
论文摘要
2020年，Sang，Shi和Yee发现了Andrews的结果的过度分区，涉及Rogers-Ramanujan-Gordon身份的平等。他们的结果部分回答了安德鲁斯的公开问题。一个开放的问题是涉及均等的过度分区身份。我们将Sang，Shi和Yee的作品扩展到任意模量，并在其身份中提供丢失的案例。我们还统一了由于LoveJoy和Chen等人而导致的Rogers-Ramanujan-Gordon身份的证明。 Sang，Shi和Yee的结果；和我们的。尽管为简短提供了验证类型的证明，但绘制了分区生成函数之间功能方程的解决方案的构造。
Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews' results involving parity in Rogers-Ramanujan-Gordon identities. Their result partially answered an open question of Andrews'. The open question was to involve parity in overpartition identities. We extend Sang, Shi, and Yee's work to arbitrary moduli, and also provide a missing case in their identities. We also unify proofs of Rogers-Ramanujan-Gordon identities for overpartitions due to Lovejoy and Chen et.al.; Sang, Shi, and Yee's results; and ours. Although verification type proofs are given for brevity, a construction of series as solutions of functional equations between partition generating functions is sketched.
