本书的目的是介绍那些非凡的数字。再讨论数字本身之后，将看到卡塔兰数计算的更卓越的组合产物。本书是按主题编排的，这从目录中就可以看出。例如，其中一章专门讨论卡塔兰数和树状图，另一章专门讨论卡塔兰数和排列。

1 Introduction
TheBinaryDecompositionModel
Counting by Characterization
Words Over an Alphabet
Some Notation
2 Dyck Words
Bertrand’S Ballot Problem
Counting Paths
Monotonic Paths
Dyck Paths
3 The Catalan Numbers
Basic Properties ofthe Catalan Numbers
Integral Representation
Recurrence Relation and Generating Function
Generating Function
4 Catalan Numbers and Paths
Monotone Paths
Dyck Paths
Path Summary
5 Catalan Numbers and Trees
Ordered Trees
Binary Trees
Full Binary Trees
Noncrossing，Alternating Trees
Tree Summary
6 CatalanNumbers andGeometricWidgits
Nonintersecting Chords
Tilings of a Staircase
Noncrossing，Alternating Chords
Triangulations of a Convex Polygon
Disk Stacking
Geometric Widgit Summary
7 CatalanNumbers andAlgebraicWidgits
Correct Parenthesizing Under a Nonassoci live
Binary Operation
Balanced Parentheses
NuU Sums in Zn+1
Algebraic Widgit Summary
8 Catalan Numbers and Interval Structures
Separated Families ofIntervals
Covenng Antichains in Int([n]1)
Antichains in Int([n-1])
Interval Summary
9 Catalan Numbers and Partitions
Noncrossing Partitions
Noncrossing Partitions and Davenport—Schinzel Sequences
DS Sequences and Partitions
Counting MNDS Sequences
Partition Summary
10 Catalan Numbers and Permutations
Permutations Obrained from Stacks and Queues
Stack Permutations
Stack.Sortable Permutations
321一Avoiding and 123一Avoiding Permutations
Permutation Summary
11 Catalan Numbers and Semiorders
The Definition of Semiorder
Characterization by Maximal Completely
Indif_ferent Subsets
Canonical Forms for Semiordered Sets
More on Semiorders
Characterization bv F0rbidden Subposet
Characterization by Unit Interval Order
Semiorder Summary
Recap
Exercises
Solutions and Hints
Appendix
Index
编辑手记