University of Illinois Urbana-Champaign

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.
Graduation Semester
2014-08
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http://hdl.handle.net/2142/50750
Copyright and License Information
Copyright 2014 Wipawee Tangjai

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