Combinatorial models for computations with formal power series

✍ Scribed by Andrew R. Maynard

• Year: 2000
• Tongue: English
• Leaves: 125
• Series: PhD thesis at University of Manchester
• Category: Library

✦ Table of Contents

Abstract 6
Declaration 7
Copyright 8
Acknowledgements 9
The Author 10
1 Introduction 12
2 Background and Definitions 17
2.1 P o sets ..................................................................................................... 17
2.2 Run Decomposition ............................................................................... 20
2.3 Avoidance Partitions and W irings ....................................................... 22
2.4 Combinatorial Correspondences ......................................................... 27
2.5 Infinite Lower Triangular Matrices...................................................... 40
2.6 The Landweber-Novikov A lgebra ....................................................... 49
3 Functional Inversion 51
3.1 Combinatorial Objects for Functional Reversion ............................ 53
3.2 Combinatorial Bijections ...................................................................... 64
4 Functional Composition 70
4.1 Combinatorial Objects for Functional Composition ........................ 71
4.2 Combinatorial Bijections ...................................................................... 77
5 Cell-Sets 79
5.1 Generalities on Cell-Sets ...................................................................... 79
5.2 The Cohomology of (CP1)1 1 ................................................................ 85
5.3 Bounded Flag Manifolds ...................................................................... 88
5.4 Combinatorial Models for the Coproduct ......................................... 97
5.5 Further Properties of the Posets Pn ...................... 102
6 Interval Coproduct 104
6.1 Interval Cell-Sets ...................................................................................... 104
6.2 The Lattice of Non-Crossing Partitions ................................................ 105
A Numbers and Formulae 114
A.l Catalan and Motzkin Numbers ............................................................. 114
A .2 Catalan Powers ............... 116
A.3 Narayana Numbers ................................................................................... 117
A.4 Fuss Numbers ............................................................................................. 119
Bibliography 122