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Partproducts of random integer compositions
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http://hdl.handle.net/1860/3855

Title:  Partproducts of random integer compositions 
Authors:  Shapcott, Caroline J. 
Keywords:  Mathematics;Integer compositions;Restricted compositions 
Issue Date:  Mar2012 
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+; 1free compositions, where S = Z+nf1g; and Srestricted 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 partproduct and its logarithm and then proceed to the more challenging problem of proving that the partproduct 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 1free and Srestricted compositions respectively. 
Description:  Thesis (PhD, Mathematics)Drexel University, 2012. 
URI:  http://hdl.handle.net/1860/3855 
Appears in Collections:  Drexel Theses and Dissertations

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