Arithmetic Properties of Partition k-tuples with Odd Parts Distinct
M. S. Mahadeva Naika and D. S. Gireesh
Department of Mathematics
Central College Campus
Let pod-k(n) denote the number of partition
k-tuples of n wherein odd parts are distinct (and even
parts are unrestricted). We establish some interesting infinite
families of congruences and internal congruences modulo 4, 16, and 5
for pod-2(n), pod-4(n), and
pod-6(n), respectively. We also find Ramanujan-type
congruences modulo 5 for pod-3(n) and densities of
pod-4(n), and pod-6(n) modulo 4, 5,
16, and 5, respectively.
Full version: pdf,
(Concerned with sequences
Received November 4 2015; revised version received April 18 2016; May 28 2016.
Published in Journal of Integer Sequences, June 4 2016.
Journal of Integer Sequences home page