The Ramanujan Journal

, Volume 40, Issue 3, pp 649–668 | Cite as

New congruences for \(\ell \)-regular partitions for \(\ell \in \{5,6,7,49\}\)

  • Zakir Ahmed
  • Nayandeep Deka Baruah


We find several new congruences for \(\ell \)-regular partitions for \(\ell \in \{5,6,7,49\}\) and also find alternative proofs of the congruences for 10- and 20-regular partitions which were proved earlier by Carlson and Webb (Ramanujan J 33:329–337, 2014) by using the theory of modular forms. We use certain p-dissections of \((q;q)_{\infty }\), \(\psi (q)\), \((q;q)_{\infty }^3\) and \(\psi (q^2)(q;q)_{\infty }^2\).


\(\ell \)-Regular partition p-Dissection Congruence 

Mathematics Subject Classification

Primary 11P83 Secondary 05A15 05A17 



The authors thank the anonymous referee for his/her insightful comments.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTezpur UniversitySonitpurIndia

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