Quaestiones Mathematicae

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

Xiaorong Li, Olivia X.M. Yao


In a recent work, Andrews dened the singular overpartition functions, denoted by C̄k;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 C̄k;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 C̄3;1(n) and innite families of congruences modulo 4 and 8 for C̄6;2(n), C̄12;3(n), C̄28;7(n).

Mathematics Subject Classication (2010): 11P83, 05A17.

Key words: Congruence, singular overpartition, theta function.
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