Monotonicity of permanents of certain doubly stochastic matrices
David London · Pacific Journal of Mathematics · 1981
Let p k (A), k = 1, , n, denote the sum of the permanents of all & X & submatrices of the n X n matrix A.We prove that where I n and P n are respectively the n x n identity matrix and the n X n permutation matrix with l's in positions (1, 2), (2, 3), , (n -1, n), (n, 1).Using (*), we prove that for n Ξ> 3 and A = (J n + PJ/2, the functions are strictly monotonic increasing in the interval 0 ^ θ :g 1.Here / n is the n X n matrix all whose entries are equal to 1/n.