The Birkhoff polytope Bn, also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph K n , n {\displaystyle K_{n,n}} , is the convex polytope in RN (where N = n²) whose points are the doubly stochastic matrices, i.e., the n × n matrices whose entries are non-negative real numbers and whose rows and columns each add up to 1. == Properties == === Vertices === The Birkhoff polytope has ...