When we establish a one-to-one or many-to-one relationship, we can call it mapping. For example, we map a spouse to his/her spouse or each child to its parent. But what would be the verb singifying an establishment of a many-to-many relationship, underlining that it is not a 1+ to 1 relationship?
you can distribute, permute, or combine multiple groups to define many to many relationships. Mapping a group to other groups does not explicitly state if the members are crossed or not, like in a Cartesian product.
Permute is a more specific case because the order matters, but both permutations and combinations are the result of distributing a set among other sets (or groups among other groups).