Some New Congruences for Andrews’ Singular Overpartition Pairs

In a recent work, Andrews defined the combinatorial objects called singular overpartitions denoted by C¯ k,i(n) , which count the number of overpartitions of n in which no part is divisible by k and only parts congruent to ± i modulo k may be overlined. Many authors have found congruences and infinite families of congruences modulo powers of 2 and 3. In this paper, we find some new infinite families of congruences for C¯1,26(n) modulo 27 and congruences modulo 4 for C¯1,512(n), C¯3,39(n) and C¯5,515(n). © 2018, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.