Patryk Gozdur: Multi-Avoidance of Permutation Patterns

Abstract.

Permutation patterns is an interesting and niche branch of mathematics that give rise to many fascinating sequences ranging from simple combinatorial operations all the way to the Catalan and Fibonacci numbers. In this thesis we study the basics of permutation patterns and prove some of the more well-known results that have been discovered during the last century. We look at permutation patterns from a more combinatorial approach rather than an algorithmical approach that is more common as seen in the works of Donald Knuth. We cover avoidance of permutation patterns and explore multi-avoidance and the kind of sequences that occur as a result of patterns avoiding more than two 3-patterns.