www.drexel.edu DREXEL UNIVERSITY LIBRARIES HOMEPAGE >> DREXEL ARCHIVES >>

iDEA: Drexel E-repository and Archives > Drexel Theses and Dissertations > Drexel Theses and Dissertations > Part-products of random integer compositions

 Please use this identifier to cite or link to this item: `http://hdl.handle.net/1860/3855`

 Title: Part-products of random integer compositions Authors: Shapcott, Caroline J. Keywords: Mathematics;Integer compositions;Restricted compositions Issue Date: Mar-2012 Abstract: A composition of n is a sequence of positive integers, called parts, that sum to n. Given a set S of positive integers, we consider compositions chosen randomly from a uniform distribution on the set of all compositions of n with parts in S. Three progressively more di cult choices of S are considered: unrestricted compositions, where S = Z+; 1-free compositions, where S = Z+nf1g; and S-restricted compositions, where S is an arbitrary co nite subset of Z+. For each choice of S, we regard the product of the parts as a random variable. We begin by deriving formulas for the moments of both the part-product and its logarithm and then proceed to the more challenging problem of proving that the part-product is asymptotically lognormal. In the case of unrestricted compositions, the calculations are relatively easy to complete using classical methods. However, those methods break down for the remaining two choices of S. We therefore introduce and formalize two new techniques for studying random compositions, the \embedding" technique and the \blocking" technique, which lead to proofs of the asymptotic lognormality of the product of parts for 1-free and S-restricted compositions respectively. Description: Thesis (PhD, Mathematics)--Drexel University, 2012. URI: http://hdl.handle.net/1860/3855 Appears in Collections: Drexel Theses and Dissertations

Files in This Item:

File Description SizeFormat