The Frobenius theorem for ${\mathbb{Z}}_2^n$-supermanifolds

We continue the development of ${\mathbb{Z}}_2^n$-supergeometry, a natural generalization of classical (${\mathbb{Z}}_2$-graded) supergeometry, by proving the Frobenius theorem for integrable distributions on differentiable ${\mathbb{Z}}_2^n$-supermanifolds. Both the local and global versions of the theorem are addressed.