Geodesic
Congruences modulo small powers of 2 and 3 for partitions into odd designated summands
Journal of integer sequences, Tome 20 (2017) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
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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/