Density results for the parity of (4k,k)-singular overpartitions

Abstract

The (k,i)-singular overpartitions, combinatorial objects introduced by Andrews in 2015, are known to satisfy Ramanujan-type congruences modulo any power of prime coprime to 6k. In this paper we consider the parity of the number C‾k,i(n) of (k,i)-singular overpartitions of n. In particular, we give a sufficient condition on even values of k so that the values of C‾4k,k(n) are almost always even. Furthermore, we show that for odd values of k≤23, k≠19, certain subsequences of C‾4k,k(n) are almost always even.