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.
DOI
https://doi.org/10.31274/etd-180810-4577
Copyright Owner
Kirsten Ann Hogenson
Copyright Date
2016
Language
en
File Format
application/pdf
File Size
60 pages
Recommended Citation
Hogenson, Kirsten Ann, "Random and deterministic versions of extremal poset problems" (2016). Graduate Theses and Dissertations. 14971.
https://lib.dr.iastate.edu/etd/14971
