
Contents
Foreword
Preface to the First Edition
Preface to the Second Edition
Acknowledgments
No Way around It. Introduction. 1
1 In One Line and Close. Permutations as Linear Orders. 3
1.1 Descents .............................. 3
1.1.1 TheDefinitionofDescents................ 3
1.1.2 EulerianNumbers .................... 4
1.1.3 Stirling Numbers and Eulerian Numbers . . . . . . . . 11
1.1.4 Generating Functions and Eulerian Numbers . . . . . 14
1.1.5 The Sequence of Eulerian Numbers . . . . . . . . . . . 16
1.2 AlternatingRuns ......................... 25
1.3 Alternating Subsequences . . . . . . . . . . . . . . . . . . . . 32
1.3.1 Definitions and a Recurrence ...