Abstract
Recently, Ramanujan’s modular equations have been applied by N.D. Baruah and B.C. Berndt to obtain a linear relation for 5-core partitions and by A. Berkovich and H. Yesilyurt to obtain inequalities for 7-core partitions. In this paper, we generalize their results by using the theory of modular forms. In particular, we prove conjectures of Berkovich and Yesilyurt.
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