ABSTRACT
This chapter is a personal account about some aspects of permutation matrices and some of their generalizations, including signed permutation matrices, alternating sign matrices, and alternating sign hypermatrices, a special case of which are latin squares. Permutations are the most basic of combinatorial constructs. They correspond to bijections between two sets of the same size. Permutations in another form give permutation matrices and they form the backbone of combinatorial matrix theory. Permutations and permutation matrices have played a substantial role in many of the talks given at each of the meetings of the Southeastern Combinatorics Conferences and were featured frequently in plenary lectures.
