Patterns in Permutations and Involutions: A Structural and Enumerative Approach

Abstract

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition leads to increasingly deep and significant line of research. The use of geometric structural reasoning, coupled with analytic and probabilistic techniques, provides a concrete framework from which to develop new enumerative techniques and forms the underlying foundation to this study.

arXiv commentPhD Dissertation, 118 pages, 30 figures

References in corpus (13)

• Small permutation classes
• On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia
• Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns
• Permutation classes of every growth rate above 2.48188
• A new upper bound for 1324-avoiding permutations
• On the topology of the permutation pattern poset
• Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005
• Pattern-Avoiding Involutions: Exact and Asymptotic Enumeration
• Growth rates for subclasses of Av(321)
• The dinner table problem: the rectangular case
• Permutations Containing Many Patterns
• Total occurrence statistics on restricted permutations
• Two Vignettes On Full Rook Placements