Counting square free monomial cremona maps

We give a complete list of square-free Cremona maps with at most six variables, up to equivalence classes. We also build an algorithm to count monomial square-free Cremona transformations. Using this algorithm, we obtain a complete list of monomial square-free Cremona transformations in seven variables.
Comment: 24 pages, 81 figures. arXiv admin note: substantial text overlap with arXiv:1509.06699