#### Date of Award

Spring 1-1-2016

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### First Advisor

Agnes Szendrei

#### Second Advisor

Peter Mayr

#### Third Advisor

Keith Kearnes

#### Fourth Advisor

Don Monk

#### Fifth Advisor

Fabio Somenzi

#### Abstract

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders. Using a recent Ramsey-theoretic technique, we determine 13 finitary operations which generate the minimal polymorphism clones containing the automorphism group of the random permutation; we call such operations minimal functions. We also show that every reduct of the random permutation is model-complete and, answering a problem stated by Peter Cameron in 2002, we prove that there are 39 closed groups containing the automorphism group of the random permutation.

#### Recommended Citation

Linman, Julie, "Minimal functions on the random permutation" (2016). *Mathematics Graduate Theses & Dissertations*. 40.

https://scholar.colorado.edu/math_gradetds/40