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Title: | Density and spacing properties of some families of non-standard 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 Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | Combinatorial number theory
Digital representation non-standard digit sets ternary representations generating functions sequences subsets of integers |
Abstract: | In this dissertation, we study a family of non-standard 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: | 2014-09-16 |
URI: | http://hdl.handle.net/2142/50750 |
Rights Information: | Copyright 2014 Wipawee Tangjai |
Date Available in IDEALS: | 2014-09-16 |
Date Deposited: | 2014-08 |
This item appears in the following Collection(s)
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois