Discrete Mathematics and Combinatorics Commons^™

Omnisculptures., Cihan Eroglu

Electronic Theses and Dissertations

In this thesis we will study conditions for the existence of minimal sized omnipatterns in higher dimensions. We will introduce recent work conducted on one dimensional and two dimensional patterns known as omnisequences and omnimosaics, respectively. These have been studied by Abraham et al [3] and Banks et al [2]. The three dimensional patterns we study are called omnisculptures, and will be the focus of this thesis. A (K,a) omnisequence of length n is a string of letters that contains each of the a^k words of length k over [A]={1,2,...a} as a substring. …