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

In a recent work, Andrews dened the singular overpartition functions, 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 ≡±i (mod k ) may be overlined. Moreover, many congruences modulo 3, 9 and congruences modulo powers of 2 for C k;i ( n ) 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 innite families of congruences modulo 27 for C 3;1 ( n ) and innite families of congruences modulo 4 and 8 for C 6;2 ( n ), C 12;3 ( n ), C 28;7 ( n ). Mathematics Subject Classication (2010): 11P83, 05A17. Key words: Congruence, singular overpartition, theta function.