ABSTRACT
This chapter gives the basic definitions and facts about permutations that are needed to discuss determinants and multilinear algebra. First we discuss how composition of functions confers a group structure on the set Sn of permutations of {1, 2, . . . , n}. Next we introduce a way of visualizing a function using a directed graph, which leads to a description of permutations in terms of disjoint directed cycles. We use this description to obtain some algebraic factorizations of permutations in the group Sn. The chapter concludes by studying inversions of functions and permutations, which give information about how many steps it takes to sort a list into increasing order. We use inversions to define the sign of a permutation, which will play a critical role in our subsequent treatment of determinants (Chapter 5).
