On the computation of Kronecker coefficients I: column-row polytopes

We present a way of computing Kronecker coefficients that uses a new family of rational convex polytopes, called column-row polytopes. We give several different formulas for the computation. They are alternating sums of numbers of integer points of either column-row polytopes or faces of column-row polytopes. We also compute the maximal dimension of these polytopes and give new proofs of some known results of more theoretical nature.