In this note we investigate the function
\(B_{k,\ell }(n)\), which counts the number of
\((k,\ell )\)-regular bipartitions of
n. We shall prove an infinite family of congruences modulo 11: for
\(\alpha \ge 2\) and
\(n\ge 0\),
$$\begin{aligned} B_{3,11}\left( 3^{\alpha }n+\frac{5\cdot 3^{\alpha -1}-1}{2}\right) \equiv 0\ (\mathrm{mod\ }11). \end{aligned}$$