A short proof of an inequality for the permanent function
Peter M. Gibson · Proceedings of the American Mathematical Society · 1966
It was brought to our attention by Marcus and Minc [2] that Brualdi and Newman have proved this theorem. Indeed, two proofs of this theorem are contained in a paper that will appear in the Oxford Quarterly [1]. The proof that we shall give, shorter than and quite different from the Brualdi-Newman proofs, shows that this theorem is almost a corollary of the Ryser representation of the permanent. Let B be an n-square matrix and let Br denote a matrix obtained from B by replacing some r columns of B by zero columns. Let S(Br) be the product of the row sums of the matrix Br. Ryser [3 ] has proved that the permanent of B is given by