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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


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