Armstrong D. Generalized noncrossing partitions and combinatorics of coxeter groups. - Providence, R.I.: American Mathematical Society, 2009. - ix, 159 p.: ill. - (Memoirs of the American Mathematical Society; Vol.202, N949). - Bibliogr.: p.155-159. - ISBN 978-0-8218-4490-8; ISSN 0065-9266  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Acknowledgements ............................................... ix Chapter 1. Introduction ......................................... 1 1.1 Coxeter-Catalan combinatorics .............................. 1 1.2 Noncrossing motivation ..................................... 6 1.3 Outline of the memoir ...................................... 9 Chapter 2. Coxeter Groups and Noncrossing Partitions ........... 13 2.1 Coxeter systems ........................................... 13 2.2 Root systems .............................................. 16 2.3 Reduced words and weak order .............................. 19 2.4 Absolute order ............................................ 22 2.5 Shifting and local self-duality ........................... 26 2.6 Coxeter elements and noncrossing partitions ............... 29 2.7 Invariant theory and Catalan numbers ...................... 35 Chapter 3. k-Divisible Noncrossing Partitions .................. 41 3.1 Minimal factorizations .................................... 41 3.2 Multichains and delta sequences ........................... 42 3.3 Definition of k-divisible noncrossing partitions .......... 46 3.4 Basic properties of k-divisible noncrossing partitions .... 48 3.5 Fuss-Catalan and Fuss-Narayana numbers .................... 59 3.6 The iterated construction and chain enumeration ........... 66 3.7 Shellability and Euler characteristics .................... 72 Chapter 4. The Classical Types ................................. 81 4.1 Classical noncrossing partitions .......................... 81 4.2 The classical Kreweras complement ......................... 87 4.3 Classical k-divisible noncrossing partitions .............. 92 4.4 Type A ................................................... 102 4.5 Type В ................................................... 104 4.6 Type D ................................................... 111 Chapter 5. Fuss-Catalan Combinatorics ......................... 115 5.1 Nonnesting partitions .................................... 115 5.2 Cluster complexes ........................................ 128 5.3 Chapoton triangles ....................................... 143 5.4 Future directions ........................................ 147 Bibliography .................................................. 155