Current Search: Combinatorial enumeration problems (x)
View All Items
 Title
 Multivariate finite operator calculus applied to counting ballot paths containing patterns [electronic resource].
 Creator
 Sullivan, Shaun, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Counting lattice paths where the number of occurrences of a given pattern is monitored requires a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of ! and " steps determine the recursion formula. In the case of ballot paths, that is paths the stay weakly above the line y = x, the solutions to the recursions are typically polynomial...
Show moreCounting lattice paths where the number of occurrences of a given pattern is monitored requires a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of ! and " steps determine the recursion formula. In the case of ballot paths, that is paths the stay weakly above the line y = x, the solutions to the recursions are typically polynomial sequences. The objects of Finite Operator Calculus are polynomial sequences, thus the theory can be used to solve the recursions. The theory of Finite Operator Calculus is strengthened and extended to the multivariate setting in order to obtain solutions, and to prepare for future applications.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3174076
 Subject Headings
 Combinatorial probabilities, Lattice paths, Combinatorial enumeration problems, Generating functions
 Format
 Document (PDF)
 Title
 Algebraic and combinatorial aspects of group factorizations.
 Creator
 Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the socalled free mappings, a powerful tool for factorization of a wide class of abelian and nonabelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
Show less  Date Issued
 2008
 PURL
 http://purl.flvc.org/FAU/107805
 Subject Headings
 Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
 Format
 Document (PDF)
 Title
 Geometric Representation of Continued Fractions.
 Creator
 Escuder, Ana, Peitgen, HeinzOtto, Florida Atlantic University
 Abstract/Description

The theory of continued fractions goes possibly as far back as 300 B.C. to Euclid. Some consider continued fractions as part of the "lost mathematics". I came across continued fractions for the first time while taking a graduate math class and I was amazed as how beautiful the representation of some numbers were using them and also how easy it was to understand the theory by making pictures. As an educator, I want to share this knowledge with my students and make it something that they could...
Show moreThe theory of continued fractions goes possibly as far back as 300 B.C. to Euclid. Some consider continued fractions as part of the "lost mathematics". I came across continued fractions for the first time while taking a graduate math class and I was amazed as how beautiful the representation of some numbers were using them and also how easy it was to understand the theory by making pictures. As an educator, I want to share this knowledge with my students and make it something that they could discover, manipulate, and appreciate. This paper is divided m three sections. The first deals with the basic theory and definitions of continued fractions. The second shows how to use technology, especially Dynamic Geometry Software to make the basic theory accessible to students in middle and high school. The third section gives some reflections of my experience working with students on continued fractions.
Show less  Date Issued
 2007
 PURL
 http://purl.flvc.org/fau/fd/FA00000751
 Subject Headings
 Combinatorial enumeration problems, Continued fractions, Metric spaces, Approximation theory
 Format
 Document (PDF)