Some congruences modulo 2, 8 and 12 for Andrews' singular overpartitions
Abstract
Recently, G. E. Andrews defined combinatorial objects which he called 
-singular overpartitions, overpartitions of 
in which no part is divisible by 
and only parts 
may be overlined. Let the number of -singular overpartitions of be\linebreak denoted by 
. Andrews and Chen, Hirschhorn and Sellers noted numerous congruences modulo 
for 
. The object of this paper is to obtain new congruences modulo for 
and modulo 
and 
for .
-singular overpartitions, overpartitions of in which no part is divisible by and only parts may be overlined. Let the number of -singular overpartitions of be\linebreak denoted by . Andrews and Chen, Hirschhorn and Sellers noted numerous congruences modulo for . The object of this paper is to obtain new congruences modulo for and modulo and for .DOI Code:
10.1285/i15900932v38n1p101
Keywords:
singular overpartition; congruence; generating function; sums of squares
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