Pattern-avoiding Permutations And Dyck Paths

Permutations with forbidden patterns have been extensively studied in past twenty years. In this thesis we deal with the discordant pattern-avoiding permutations and alternating pattern-avoiding permutations. The contents of this thesis is arranged as follows.In the first chapter, we give the development of the theories of combinatorial se-quences and Dyck paths in briefly.In the second chapter, we present the basic definition of the combinatorial sequences and Dyck paths. We introduce the definitions of discordant permutations, the alternating permutations and Dyck paths.In the third chapter. we studied the k-discordant pattern-avoiding permutations and give the classification of the2-discordant τ-avoiding permutations(τ∈S3).In the fourth chapter, we focus enumerating some kinds of alternating pattern-avoiding permutations. We establish the bisections between some kinds of alternating pattern-avoiding permutations and Dyck paths.