Abstract
dc:descriptionIn this dissertation we present a number of new results in combinatorial number theory. Chapter I discusses a generalization of B(,2)-sequences which are used in Chapter II and Chapter III to obtain short interval results about k-free values of irreducible polynomials. Chapter IV deals with the number of partitions of an integer using a set of distinct parts; Chapter V demonstrates how a single prime value of a polynomial with non-negative coefficients can be used to show that the polynomial is irreducible; Chapter VI compares simple continued fraction convergents for SQRT.(N) with Newton approximations to SQRT.(N); and Chapter VII obtains exact formulas for a certain class of ballot problems. An introduction is included which gives preliminary discussions on various aspects of the problems.
Degree
thesis:*- 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 and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Filaseta, Michael Anthony
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8502140
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/71225