Combinatorics of Permutations, 2nd Edition

No Way around It. Introduction.

This book is devoted to the study of permutations. While the overwhelming

majority of readers already know what they are, we are going to define them

for the sake of completeness. Note that this is by no means the only definition

possible.

DEFINITION 0.1 A linear ordering of the elements of the set [n]=

{1, 2, 3, ···,n} is called a permutation, or, if we want to stress the fact that

it consists of n entries, an n-permutation.

In other words, a permutation lists all elements of [n]sothateachelement

is listed exactly once.

Example 0.2

If n = 3, then the n-permutations are 123, 132, 213, 231, 312, 321.

There is nothing magic abo ...