A bipartition of $n$ is an ordered pair of partitions $(\lambda,\mu)$ such that the sum of all of the parts equals $n$. In this article, we concentrate on the function $c_5(n)$, which counts the number of bipartitions $(\lambda,\mu)$ of $n$ subject to the restriction that each part of $\mu$ is divisible by $5$. We explicitly establish four Ramanujan type congruences and several infinite families of congruences for $c_5(n)$ modulo $3$.
@article{10_37236_5040,
author = {Jian Liu and Andrew Y.Z. Wang},
title = {Arithmetic properties of a restricted bipartition function},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/5040},
zbl = {1327.05026},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5040/}
}
TY - JOUR
AU - Jian Liu
AU - Andrew Y.Z. Wang
TI - Arithmetic properties of a restricted bipartition function
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/5040/
DO - 10.37236/5040
ID - 10_37236_5040
ER -
%0 Journal Article
%A Jian Liu
%A Andrew Y.Z. Wang
%T Arithmetic properties of a restricted bipartition function
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5040/
%R 10.37236/5040
%F 10_37236_5040
Jian Liu; Andrew Y.Z. Wang. Arithmetic properties of a restricted bipartition function. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5040
