Infinite families of congruences for m-regular [j, k]-overpartitions in two colors

T. N. Veeranayaka, M. S. Mahadeva Naika, Harishkumar T

Let aj,km(n) denote the number of overpartitions of n with two colors in which no parts are divisible by m and only parts congruent to j modulo k may be overlined. In this work, we establish many infinite families of congruences modulo powers of 2 for a1,33(n), a1,43(n) and congruences modulo powers of 2 and 3 for a1,49(n). 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 15(3) (2022), pp. 53-74