A unified approach to simple special cases of extremal permutation problems

Extremal permutation problems are combinatorial problems where an objective function has to be optimized over a set of permutations (as e.g., assignment problem) and the traveling salesman problem). In this note we propose a general approach to search for special cases of extremal permutation problems where an optimal solution can be tained in an explicit form. The approach is based on a special factorization of permutations into transpositions and on a related partial order among permutations. The approach is illustrated by several applications to assignment problems with focus on the. Quadratic assignment problem. For the Koopmans Beckmann problem, a number of sinple special cases is singled out