A generating tree approach to k-nonnesting arc diagrams

This thesis describes a strategy for exhaustively generating series information and enumerating combinatorial classes that can be represented using arc diagrams. We focus on k-nonnesting set partitions, permutations, matchings and tangled diagrams. Results are new functional equations, counting sequences, bijections and asymptotic results for these classes. Our key innovation is a generalized arc diagram in which arcs may have left endpoints, but not right endpoints, and our main tool is generating trees.