Monographie no. 42
A combinatorial miscellany
(ISBN 978-2-940264-09-4)
Anders Björner & Richard P. Stanley
softbound, 164 pages, 2010; 37 CHF
With some simplification, combinatorics can be said to be the mathematics of the finite. This monograph describes a few selected problems and results in some detail: some examples of problems from pure combinatorics, some illustrating its interactions with other parts of mathematics, and a few glimpses of its use for computer science. The book is written in a very accessible way. Even with little mathematical background the reader is introduced into the spectacular growth of combinatorics in the last few decades.
Table des matières
INTRODUCTION
CHAPTER 1 Bijective proofs
CHAPTER 2 Partitions
CHAPTER 3 Plane partitions
CHAPTER 4 Standard Young tableaux
CHAPTER 5 Connections with representation theory
CHAPTER 6 Increasing and decreasing subsequences
CHAPTER 7 Reduced decompositions
CHAPTER 8 Tilings
CHAPTER 9 Tilings and plane partitions
CHAPTER 10 The Möbius function and set partitions
CHAPTER 11 Arrangements and regions
CHAPTER 12 Face numbers of polytopes
CHAPTER 13 Connections with topology
CHAPTER 14 Extremal combinatorics
CHAPTER 15 Complexity of sorting and distinctness
CHAPTER 16 Complexity of graph properties
CHAPTER 17 Notes
BIBLIOGRAPHY
CITED MATHEMATICIANS
INDEX
