Arithmetic properties of partitions into $k$ parts congruent to $\pm l$ modulo $m$
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 47-59
MSC: Primary 11P83; Secondary 05A17.
DOI: 10.4064/cm7742-2-2019
Published online: 7 October 2019
Abstract
Ramanujan-type congruences satisfied by functions that enumerate partitions whose parts belong to a finite set are well-known and have been studied by many authors. In this paper, we let the parts belong to the infinite set of integers congruent to $\pm l$ modulo $m$ and we obtain infinitely many Ramanujan-type congruences for the corresponding number of partitions into exactly $k$ parts, $p_{\pm l}^{m}(n, k)$. We also consider two other restricted partition functions.
