New congruences for 2-color partitions

Shane Chern

doi:10.1016/j.jnt.2015.12.020

New congruences for 2-color partitions

Number Theory 2016-02-10 v2 Combinatorics

Authors: Shane Chern

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Abstract

Let $p_k(n)$ denote the number of $2$ -color partitions of $n$ where one of the colors appears only in parts that are multiples of $k$ . We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo $5$ for $p_k(n)$ . Moreover, we will present some new congruences modulo $7$ for $p_4(n)$ .

Keywords

integer partitions 2-color partitions congruences modulo 5 congruences modulo 7 number theory partition function

Cite

@article{arxiv.1511.00246,
  title  = {New congruences for 2-color partitions},
  author = {Shane Chern},
  journal= {arXiv preprint arXiv:1511.00246},
  year   = {2016}
}

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