# 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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