On some congruences for Andrews’ singular overpartitions

Abstract

Andrews’ singular overpartitions can be enumerated by Ck,i(n), the number of overpartitions of n where only parts congruent to ±i (mod k) may be overlined, and no part is divisible by k. A number of authors have studied congruences satisfied by singular overpartitions. In particular, congruences for C3,1(n) modulo 3, 8, 9, 18, 32, 36, 64, 72 and 144 have been proved. In this article, we prove new congruences modulo 108, 192, 288 and 432 for C3,1(n).