# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 1, March 2020  pp. 95–108.

Some congruences modulo power of 2 for Andrews' singular overpartition pairs

Authors:  T. Kathiravan
Author institution:School of Mathematics, IISER, Thiruvananthapuram, Kerala, India

Summary:  Recently, Andrews defined the combinatorial objects called singular overpartitions. The number of overpartitions of n in which no part is divisible by k and only parts ≡ ± i (mod k) may be overlined is denoted by C {k,i} (n). Very recently, Naika [17] has defined Andrews singular overpartition pairs. The number of singular overpartition pairs of n in which no part is divisible by δ and only parts ≡ ± i, ± j (mod δ) may be overlined is denoted by C δ {i,j} (n). In [17], Naika et~al. prove some congruences for C{3}{4,1} (n) and C{5}{4,1}(n) modulo 4. In this paper we obtain some new congruences modulo 2 for C {15} {3,6} (n) and C {42} {7,14}(n).