Congruences for the reciprocals of the Ramanujan-Gordon identities. (English) Zbl 1429.11190
Summary: We introduce two special partition functions according to two identities obtained by Ramanujan and Gordon. Using elementary generating function manipulations, we establish several Ramanujan type congruences.
MSC:
| 11P83 | Partitions; congruences and congruential restrictions |
References:
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| [2] | S. Ramanujan, On certain arithmetical functions, Trans. Cambridge Philos. Soc. 22 (1916), 159-184. [18] W.-L. Zhang and C. Wang, An unexpected Ramanujan-type congruence modulo 7 for 4-colored generalized Frobenius partitions, Ramanujan J. 44 (2017), 125-131. · Zbl 1386.05010 |
| [3] | H. Zhao and Z. Zhong, Ramanujan type congruences for a partition function, Electron. J. Combin. 18 (2011), paper 58, 9 pp. Bernard Lishuang LinAndrew Yezhou Wang School of ScienceSchool of Mathematical Sciences Jimei UniversityUniversity of Electronic Science 361021 Xiamen, P.R. Chinaand Technology of China E-mail: linlsjmu@163.com611731 Chengdu, P.R. China E-mail: yzwang@uestc.edu.cn · Zbl 1220.05006 |
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