$l$-regular bipartition

I know about $l$-regular partition. Now I came across $l$-regular bipartition/tripartition. But how are former and latter different. Where former ensures that each part in the partition is not divisible by $l$, if the latter does the same, how are they both different? This question is in the context of curiosity while studying a paper on congruences of partitions. Where could this be possibly useful?

Thank you in advance.

According to the definitions that I’ve seen, an $\ell$-regular bipartition of $n$ is an ordered pair $\langle\lambda_1,\lambda_2\rangle$ of $\ell$-regular partitions such that the sum of all of the parts of $\lambda_1$ and $\lambda_2$ is $n$. Thus,

$$\big\langle\langle 4,2,1\rangle,\langle 5,5\rangle\big\rangle$$

is a $3$-regular bipartition of $17$.

Presumably an $\ell$-regular tripartition of $n$ is an ordered triple $\langle\lambda_1,\lambda_2,\lambda_3\rangle$ of $\ell$-regular partitions such that the sum of all of the parts of $\lambda_1,\lambda_2$, and $\lambda_3$ is $n$.

Added in response to comment: There is exactly one partition of $17$ with parts $5,5,4,2$, and $1$: $\langle 5,5,4,2,1\rangle$. But these five parts can be split between two partitions in several different ways, so there are several bipartitions of $17$ with these five parts:

$$\begin{align*} &\big\langle\langle 5,4,2,1\rangle,\langle 5\rangle\big\rangle;\big\langle\langle 5\rangle,\langle 5,4,2,1\rangle\big\rangle;\\ &\big\langle\langle 5,5,2,1\rangle,\langle 4\rangle\big\rangle;\big\langle\langle 4\rangle,\langle 5,5,2,1\rangle\big\rangle;\\ &\big\langle\langle 5,5,4,1\rangle,\langle 2\rangle\big\rangle;\big\langle\langle 2\rangle,\langle 5,5,4,1\rangle\big\rangle;\\ &\big\langle\langle 5,5,4,2\rangle,\langle 1\rangle\big\rangle;\big\langle\langle 1\rangle,\langle 5,5,4,2\rangle\big\rangle;\\ &\big\langle\langle 4,2,1\rangle,\langle 5,5\rangle\big\rangle;\big\langle\langle 5,5\rangle,\langle 4,2,1\rangle\big\rangle;\\ &\big\langle\langle 5,5,4\rangle,\langle 2,1\rangle\big\rangle;\big\langle\langle 2,1\rangle,\langle 5,5,4\rangle\big\rangle;\\ &\big\langle\langle 5,5,2\rangle,\langle 4,1\rangle\big\rangle;\big\langle\langle 4,1\rangle,\langle 5,5,2\rangle\big\rangle;\\ &\big\langle\langle 5,5,1\rangle,\langle 4,2\rangle\big\rangle;\big\langle\langle 4,2\rangle,\langle 5,5,1\rangle\big\rangle;\\ &\big\langle\langle 5,4,2\rangle,\langle 5,1\rangle\big\rangle;\big\langle\langle 5,1\rangle,\langle 5,4,2\rangle\big\rangle;\\ &\big\langle\langle 5,4,1\rangle,\langle 5,2\rangle\big\rangle;\big\langle\langle 5,2\rangle,\langle 5,4,1\rangle\big\rangle;\\ &\big\langle\langle 5,2,1\rangle,\langle 5,4\rangle\big\rangle;\big\langle\langle 5,4\rangle,\langle 5,2,1\rangle\big\rangle\,. \end{align*}$$

That’s $22$ bipartitions with the same five parts, assuming that I didn’t miss any.