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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
- Date of Ingest
- 2014-09-16T17:26:10Z
- 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
- Permalink
- http://hdl.handle.net/2142/50750
- Copyright and License Information
- Copyright 2014 Wipawee Tangjai
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