EXTENDING RECENT PARITY RESULTS OF NYIRENDA AND MUGWANGWAVARI FOR PARTITIONS WITH INITIAL REPETITIONS

Recently, Nyirenda and Mugwangwavari considered several restricted partition functions which they viewed from the perspective of partitions with initial repetitions. Utilizing a number of results from Slater, along with classical generating function manipulations, they proved several Ramanujan–like congruences modulo 2 satisfied by these functions. Our goal in this note is to establish infinite families of Ramanujan-type congruences for these functions that have the aforementioned congruences as special cases.