Density and spacing properties of some families of non-standard ternary representations
Tangjai, Wipawee
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https://hdl.handle.net/2142/50750
Description
Title
Density and spacing properties of some families of non-standard ternary representations
Author(s)
Tangjai, Wipawee
Issue Date
2014-09-16
Director of Research (if dissertation) or Advisor (if thesis)
Reznick, Bruce A.
Doctoral Committee Chair(s)
Hildebrand, A.J.
Boca, Florin
Committee Member(s)
Reznick, Bruce A.
Ahlgren, Scott
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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