  One studies Cremona monomial maps by combinatorial means. Among the results
is a simple integer matrix theoretic proof that the inverse of a Cremona
monomial map is also defined by monomials of fixed degree, and moreover, the
set of monomials defining the inverse can be obtained explicitly in terms of
the initial data. A neat consequence is drawn for the plane Cremona monomial
group, in particular the known result saying that a plane Cremona (monomial)
map and its inverse have the same degree. Included is a discussion about the
computational side and/or implementation of the combinatorial invariants
stemming from these questions.
