Author(s): Kimmo Eriksson
Series: PhD thesis at Kungl Tekniska Högskolan
Publisher: KTH Stockholm
Year: 1993
TItle
Abstract
Sammanfattning
Contents
Preface
Part I: Strong convergence
Chapter 1. What is strong convergence?
1.1. Combinatorial games
1.2. A characterization of strong convergence
1.3. Game languages
1.4. Greedoids
Chapter 2. Examples of strong convergence
2.1. The bubble-sort game
2.2. The shelling game
2.3. The k-snake game
2.4. The chromatic game
2.5. Jeu de Taquin
2.6. The chip firing game
2.7. The poset core game
Part II: The numbers game
Chapter 3. The numbers game and strong convergence
3.1. History
3.2. The rules
3.3. Strong convergence
3.4. The edge weighted case
3.5. Divergence
3.6. Characterization of E-games
3.7. The general case
3.8. When is (xyx...)_n [same result as] (yxy...)_n?
3.9. Divergence
3.10. Characterization of N-games
Chapter 4. The language of legal play
4.1. The language of legal play
4.2. When is alpha [same result as] beta in an E-game?
4.3. The comparison theorem
4.4. The language of legal play is a greedoid
Chapter 5. Deciding reachability
5.1. The Perron-Frobenius theorem
5.2. The Moore-Penrose pseudoinverse
5.3. The shot vector
5.4. Reachability is decidable for rational positions in Mozes games
5.5. A game where all p_x tend to 0
Chapter 6. Classification of finite games and looping games
6.1. Looping U-games
6.2. Loopers have largest eigenvalue 2
6.3. Looping E-games
6.4. Symmetric weights
6.5. Nonsymmetric weights
6.6. Looping games
6.7. Finite games
6.8. Looping N-games
6.9. The dual E-game
Part III: Coxeter groups and the numbers game
Chapter 7. Coxeter groups
7.1. Coxeter groups
7.2. Words in the generators
7.3. Weak order and Bruhat order
7.4. The canonical geometric representation
Chapter 8. Connections between Coxeter groups and the numbers game
8.1. Every E-game represents a Coxeter group
8.2. Basic connections
8.3. Geometry of games and groups
8.4. Finite groups and affine groups — subloopers and loopers
8.5. Groups of general N-games
Chapter 9. Polygon posets
9.1. Introduction
9.2. Polygon posets and the weak order
9.3. The weak order is a semilattice
9.4. Polygon posets are ideals in the weak order
9.5. Polygon posets and generalized quotients
9.6. The Bruhat order on polygon posets
9.7. Sharp quotients
9.8. FSA recognizes reduced words of superhexagonal groups
9.9. Position posets and the numbers game
Index
Bibliography
