  A classical result of MacMahon states that inversion number and major index
have the same distribution over permutations of a given multiset. In this work
we prove a strengthening of this theorem originally conjectured by Haglund. Our
result can be seen as an equidistribution theorem over the ordered partitions
of a multiset into sets, which we call ordered multiset partitions. Our proof
is bijective and involves a new generalization of Carlitz's insertion method.
This generalization leads to a new extension of Macdonald polynomials for hook
shapes. We use our main theorem to show that these polynomials are symmetric
and we give their Schur expansion.
