Congruences modulo $7$ and $11$ for certain two restricted partition functions

Paper

Abstract

For an integer

, let

count the number of generalized cubic partitions of

, which are partitions of

whose even parts may appear in

different colors, and

count the number of partitions obtained by adding the links of the

-elongated plane partition diamonds of length

. We prove in this note infinite families of congruences modulo

and

for

and

by employing elementary

-series techniques. These results generalize particular congruences modulo

and

for

and

recently found by Dockery, and Baruah, Das, and Talukdar, respectively, using modular forms.