Congruences Modulo Small Powers of 2 and 3 for Partitions into Odd Designated Summands
B. Hemanthkumar
Department of Mathematics
M. S. Ramaiah University of Applied Sciences
Bengaluru-560 058
India
H. S. Sumanth Bharadwaj and M. S. Mahadeva Naika
Department of Mathematics
Central College Campus
Bangalore University
Bengaluru-560 001
India
Abstract:
Andrews, Lewis and Lovejoy introduced a new class of partitions,
partitions with designated summands. Let PD(n) denote the number of
partitions of n with designated summands and PDO(n) denote the number
of partitions of n with designated summands in which all parts are odd.
Andrews et al. established many congruences modulo 3 for PDO(n) by
using the theory of modular forms. Baruah and Ojah obtained numerous
congruences modulo 3, 4, 8 and 16 for PDO(n) by using theta function
identities. In this paper, we prove several infinite families of
congruences modulo 9, 16 and 32 for PDO(n).
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(Concerned with sequences
A077285
A102186.)
Received October 25 2016; revised version received January 13 2017; January 23 2017.
Published in Journal of Integer Sequences, January 28 2017.
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