The Rogers-Ramanujan-Gordon identities, the generalized G?llnitz-Gordon identities, and parity questions

Kim S.; Yee A.J.

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The Rogers-Ramanujan-Gordon identities, the generalized G?llnitz-Gordon identities, and parity questions

机译：Rogers-Ramanujan-Gordon身份，广义G？llnitz-Gordon身份和奇偶性问题

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Recently, George Andrews investigated a variety of parity questions in classical partition identities. In particular, he involved parity restrictions in the Rogers-Ramanujan-Gordon identities. In this paper, we reveal the relationship of his results with Bressoud's generalization of the Rogers-Ramanujan-Gordon identities. In addition, Andrews observed that one case of his identities is related to the G?llnitz-Gordon identities. In the light of the fact that the G?llnitz-Gordon identities are special cases of a general partition theorem of Andrews, we extend Andrews' identities by generalizing his observation. We also provide a generating function of the missing case of his identities.

机译：最近，乔治·安德鲁斯（George Andrews）研究了经典分区身份中的各种奇偶性问题。特别是，他在Rogers-Ramanujan-Gordon身份中涉及均等限制。在本文中，我们揭示了他的结果与Bressoud对Rogers-Ramanujan-Gordon身份的推广的关系。此外，安德鲁斯（Andrews）观察到他的一个身份与G？llnitz-Gordon身份有关。鉴于G？llnitz-Gordon身份是安德鲁斯一般分割定理的特例，我们通过推广安德鲁斯的观察来扩展安德鲁斯的身份。我们还提供了他的身份失踪案的生成功能。

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《Journal of Combinatorial Theory, Series A》 |2013年第5期|共19页
作者
Kim S.; Yee A.J.;
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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Integer partitions; Parity in partitions; The G?llnitz-Gordon identities; The Rogers-Ramanujan identities; The Rogers-Ramanujan-Gordon identities;

机译：整数分区;分区中的奇偶性;G？llnitz-Gordon身份;Rogers-Ramanujan身份;Rogers-Ramanujan-Gordon身份;

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The Rogers-Ramanujan-Gordon identities, the generalized G?llnitz-Gordon identities, and parity questions

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