Date

2016

Department or Program

Mathematics

Primary Wellesley Thesis Advisor

Ann Trenk

Abstract

This thesis examines several classes of interval orders arising from restrictions on the permissible interval lengths. We first provide an accessible proof of the characterization theorem for the class of interval orders representable with lengths between 1 and k for each k in {1,2,...}. We then consider the interval orders representable with lengths exactly 1 and k for k in {0,1,...}. We characterize the class of interval orders representable with lengths 0 and 1, both structurally and algorithmically. To study the other classes in this family, we consider a related problem, in which each interval has a prescribed length. We derive a necessary and sufficient condition for an interval order to have a representation with a given set of prescribed lengths. Using this result, we provide a necessary condition for an interval order to have a representation with lengths 1 and 2.

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