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Title:  Density and spacing properties of some families of nonstandard ternary representations 
Author(s):  Tangjai, Wipawee 
Director of Research:  Reznick, Bruce A. 
Doctoral Committee Chair(s):  Hildebrand, A.J.; Boca, Florin 
Doctoral Committee Member(s):  Reznick, Bruce A.; Ahlgren, Scott 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Combinatorial number theory
Digital representation nonstandard digit sets ternary representations generating functions sequences subsets of integers 
Abstract:  In this dissertation, we study a family of nonstandard digital representations in base 3. Let A be an index set such that A={0,u1,u2}, where u1 is equivalent to 1 (mod 3) and u2 is equivalent to 2 (mod 3). We study the set of integers which can be written as \sum_{i=0}^{\infty}\epsilon_i 3^i, where \epsilon_i is in A. Most of the work in this dissertation is about the case that the index set A={0,1,5}. We are particularly interested in the maximal sets of consecutive integers, the density of the represented numbers and the related generating functions. 
Issue Date:  20140916 
URI:  http://hdl.handle.net/2142/50750 
Rights Information:  Copyright 2014 Wipawee Tangjai 
Date Available in IDEALS:  20140916 
Date Deposited:  201408 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois