Behavior of the permanent of a special class of doubly stochastic matrices
Vu Anh Phuong · Linear and Multilinear Algebra · 1980
Let A be an n×n doubly stochastic matrix with at least one zero entry such that A is closest in the Euclidean norm to n , the matrix whose entries are all 1/n. Then the permanent function is monotone decreasing on the segment (1−theta;) A+θ Jn for 0 θ > 1.