D D Somashekara ; K N Vidya - On-Regular Bipartitions Modulo $m$

hrj:5106 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5106
On-Regular Bipartitions Modulo $m$

Authors: D D Somashekara ; K N Vidya

Let $b_l (n)$ denote the number of $l$-regular partitions of $n$ and $B_l (n)$ denote the number of $l$-regular bipartitions of $n$. In this paper, we establish several infinite families of congruences satisfied by $B_l (n)$ for $l \in {2, 4, 7}$. We also establish a relation between $b_9 (2n)$ and $B_3 (n)$.

Published on: January 23, 2019
Submitted on: January 23, 2019
Keywords: 05A17,Congruence,partition,regular partition,regular bipartition,theta functions 2010 Mathematics Subject Classification 11P83, [ MATH ] Mathematics [math], [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT]


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