Some congruences modulo 2, 8 and 12 for Andrews' singular overpartitions


Recently, G. E. Andrews defined combinatorial objects which he called (k,i)-singular overpartitions, overpartitions of n in which no part is divisible by k and only parts \equiv\pm i\pmod k may be overlined. Let the number of (k,i)-singular overpartitions of n be\linebreak denoted by \overline{C}_{k,i}(n). Andrews and Chen, Hirschhorn and Sellers noted numerous congruences modulo 2 for \overline{C}_{3,1}(n). The object of this paper is to obtain new congruences modulo 2 for \overline{C}_{20,5}(n) and modulo 8 and 12 for \overline{C}_{3,1}(n).

DOI Code: 10.1285/i15900932v38n1p101

Keywords: singular overpartition; congruence; generating function; sums of squares

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