New infinite families of congruences for Andrews’ (K, I)-singular overpartitions

Abstract

In a recent work, Andrews defined the singular overpartition functions, denoted by , which count the number of overpartitions of n in which no part is divisible by k and only parts ≡ ±i (mod k) may be overlined. Moreover, many congruences modulo 3, 9 and congruences modulo powers of 2 for were discovered by Ahmed and Baruah, Andrews, Chen, Hirschhorn and Sellers, Naika and Gireesh, Shen and Yao for some pair (k, i). In this paper, we proved new infinite families of congruences modulo 27 for and infinite families of congruences modulo 4 and 8 for , , .