Degree Type

Dissertation

Date of Award

2016

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Ryan R. Martin

Abstract

Let P(n) denote the set of all subsets of {1,...,n} and let P(n,p) be the set obtained from P(n) by selecting elements independently at random with probability p. The Boolean lattice is a partially ordered set, or poset, consisting of the elements of P(n), partially ordered by set inclusion. A basic question in extremal poset theory asks the following: Given a poset P, how big is the largest family of sets in the Boolean lattice which does not contain the structure P as a subposet? The following random analogue of this question is also of interest: Given a poset P, how big is the largest family of sets in P(n,p) which does not contain the structure P as a subposet? In this thesis, we present new proofs for a collection of deterministic extremal subposet problems. We also discuss a new technique called the Hypergraph Container Method in depth and use it to prove a random version of De Bonis and Katona's (r+1)-fork-free theorem.

Copyright Owner

Kirsten Ann Hogenson

Language

en

File Format

application/pdf

File Size

60 pages

Included in

Mathematics Commons

Share

COinS