Density and spacing properties of some families of non-standard ternary representations

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Tangjai, Wipawee

Contributors dc:contributor

• Reznick, Bruce A.
• Hildebrand, A.J.
• Boca, Florin
• Ahlgren, Scott

• Combinatorial number theory
• Digital representation
• non-standard digit sets
• ternary representations
• generating functions
• sequences
• subsets of integers

Statement dc:rights

• Copyright 2014 Wipawee Tangjai

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/50750

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/50750