- Title Pages
- Dedication
- Preface
- Symbols
- 1 Binomial Coefficients
- 2 The Central Binomial Coefficient
- 3 The Central Binomial Coefficient Revisited
- 4 Binomial Coefficients Revisited
- 5 Catalan Numbers
- 6 The Ubiquity of Catalan Numbers I
- 7 The Ubiquity of Catalan Numbers II
- 8 Tress and Catalan Numbers
- 9 Lattice Paths and Catalan Numbers
- 10 Partitions and Catalan Numbers
- 11 Algebra, Sports, and Catalan Numbers
- 12 Pascal' Triangle and Catalan Numbers
- 13 Divisibility Properties
- 14 A Catalan Triangle
- 15 A Family of Binary Words
- 16 Tribinomial Coefficients
- 17 Generalized Catalan Numbers
- Appendix A
- Appendix B The First 100 Catalan Numbers
- References
- Index of Mathematicians
- <i>Index</i>

# Tress and Catalan Numbers

# Tress and Catalan Numbers

- Chapter:
- (p.227) 8 Tress and Catalan Numbers
- Source:
- Catalan Numbers with Applications
- Author(s):
### Thomas Koshy

- Publisher:
- Oxford University Press

This chapter presents delightful occurrences of Catalan numbers in the theory of trees. They include binary trees, full binary trees, planted trivalent binary trees, triangulations and prefix expressions, chessboard, ordered rooted trees, forest, and ordered forests.

*Keywords:*
connected graph, forest, binary tree, full binary tree, planted trivalent binary tree, prefix expression, chessboard, Catalan triangle, Bernhard's algorithm

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- Title Pages
- Dedication
- Preface
- Symbols
- 1 Binomial Coefficients
- 2 The Central Binomial Coefficient
- 3 The Central Binomial Coefficient Revisited
- 4 Binomial Coefficients Revisited
- 5 Catalan Numbers
- 6 The Ubiquity of Catalan Numbers I
- 7 The Ubiquity of Catalan Numbers II
- 8 Tress and Catalan Numbers
- 9 Lattice Paths and Catalan Numbers
- 10 Partitions and Catalan Numbers
- 11 Algebra, Sports, and Catalan Numbers
- 12 Pascal' Triangle and Catalan Numbers
- 13 Divisibility Properties
- 14 A Catalan Triangle
- 15 A Family of Binary Words
- 16 Tribinomial Coefficients
- 17 Generalized Catalan Numbers
- Appendix A
- Appendix B The First 100 Catalan Numbers
- References
- Index of Mathematicians
- <i>Index</i>