Author(s): William Anderson Davis
Series: Master thesis at Oklahoma State University
Year: 2019
Acknowledgements ................................................................................................. iii
Abstract ................................................................................................................... iv
Table of Contents ......................................................................................................v
List of Figures ......................................................................................................... vi
1 Introduction ........................................................................................................ 1
2 Structures Counted by Catalan’s Triangle ........................................................ 5
2.1 Dyck Paths and Ballot Sequences .............................................................. 5
2.2 Pattern Avoiding Permutations ................................................................. 8
2.3 Triangulations, Parenthesizations, and Full Binary Trees .................... 10
3 Structures Counted by Borel’s Triangle .......................................................... 18
3.1 Marked Dyck Paths and Three-Party Ballot Sequences ........................ 18
3.2 Marked Triangulations, Parenthesizations, and Full Binary Trees ...... 21
3.3 More Permutations ................................................................................... 27
Bibliography ........................................................................................................... 32
VITA ....................................................................................................................... 33
