New infinite families of congruences modulo 8 for partitions with even parts distinct

Ernest X. W. Xia¹

¹Jiangsu University

The electronic journal of combinatorics, Tome 21 (2014) no. 4

Résumé

Let $ped(n)$ denote the number of partitions of an integer $n$ wherein even parts are distinct. Recently, Andrews, Hirschhorn and Sellers, Chen, and Cui and Gu have derived a number of interesting congruences modulo 2, 3 and 4 for $ped(n)$. In this paper we prove several new infinite families of congruences modulo 8 for $ped(n)$. For example, we prove that for $ \alpha \geq 0$ and $n\geq 0$,\[ ped\left(3^{4\alpha+4}n+\frac{11\times 3^{4\alpha+3}-1}{8}\right)\equiv 0 \ ({\rm mod \ 8}).\]

Détail

DOI : 10.37236/4036

Classification : 11P83, 05A17
Mots-clés : partition, congruence, regular partition