Geodesic
Congruences modulo small powers of 2 and 3 for partitions into odd designated summands
Journal of integer sequences, Tome 20 (2017) no. 4
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 $PDO(n)$.
Classification : 11P83, 05A17
Keywords: partition with designated summand, congruence, theta function 
@article{JIS_2017__20_4_a1,
     author = {Hemanthkumar,  B. and Bharadwaj,  H.S.Sumanth and Naika,  M.S.Mahadeva},
     title = {Congruences modulo small powers of 2 and 3 for partitions into odd designated summands},
     journal = {Journal of integer sequences},
     year = {2017},
     volume = {20},
     number = {4},
     zbl = {1364.11144},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a1/}
}
TY  - JOUR
AU  - Hemanthkumar,  B.
AU  - Bharadwaj,  H.S.Sumanth
AU  - Naika,  M.S.Mahadeva
TI  - Congruences modulo small powers of 2 and 3 for partitions into odd designated summands
JO  - Journal of integer sequences
PY  - 2017
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a1/
LA  - en
ID  - JIS_2017__20_4_a1
ER  - 
%0 Journal Article
%A Hemanthkumar,  B.
%A Bharadwaj,  H.S.Sumanth
%A Naika,  M.S.Mahadeva
%T Congruences modulo small powers of 2 and 3 for partitions into odd designated summands
%J Journal of integer sequences
%D 2017
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a1/
%G en
%F JIS_2017__20_4_a1
Hemanthkumar,  B.; Bharadwaj,  H.S.Sumanth; Naika,  M.S.Mahadeva. Congruences modulo small powers of 2 and 3 for partitions into odd designated summands. Journal of integer sequences, Tome 20 (2017) no. 4. http://geodesic.mathdoc.fr/item/JIS_2017__20_4_a1/