Journal of the Ramanujan Mathematical Society
Volume 35, Issue 1, March 2020 pp. 95–108.
Some congruences modulo power of 2 for Andrews' singular overpartition pairs
Authors:
T. Kathiravan
Author institution:School of Mathematics, IISER, Thiruvananthapuram, Kerala, India
Summary:
Recently, Andrews defined the combinatorial objects called
singular overpartitions. The number of overpartitions of n in
which no part is divisible by k and only parts ≡ ± i
(mod k) may be overlined is denoted by C {k,i} (n).
Very recently, Naika [17] has defined Andrews
singular overpartition pairs. The number of singular overpartition
pairs of n in which no part is divisible by δ and only
parts ≡ ± i, ± j (mod δ) may be overlined is denoted
by C δ {i,j} (n). In [17], Naika
et~al. prove some congruences for C{3}{4,1} (n) and
C{5}{4,1}(n) modulo 4. In this paper we obtain some
new congruences modulo 2 for C {15} {3,6} (n) and
C {42} {7,14}(n).
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