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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 3, September 2022  pp. 241–256.

Congruences for some partition functions

Authors:  Ankush Goswami and Abhash Kumar Jha
Author institution:School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Dr., Edinburg, TX, 78539

Summary:  Recently, Andrews carried out a thorough investigation of integer partitions in which all parts of a given parity are smaller than those of the opposite parity. Further, considering a subset of this set of partitions, he obtains several interesting arithmetic and combinatorial properties and its connections to the third order mock theta function ν(q). In this paper, we study certain congruences satisfied by the above set of partitions (and the subset above) along with a certain subset of partitions (of Andrews' partitions above) studied by Uncu. We also obtain certain family of congruences modulo 2 for the Ramanujan tau function.

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