Citation
Skarda, Ralph Vencil (1966) Some Central Limit Theorems for Doubly Restricted Partitions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YH19JH87. https://resolver.caltech.edu/CaltechTHESIS:10122015160506112
Abstract
Let P_{K, L}(N) be the number of unordered partitions of a positive integer N into K or fewer positive integer parts, each part not exceeding L. A distribution of the form
Ʃ/N≤x P_{K,L}(N)
is considered first. For any fixed K, this distribution approaches a piecewise polynomial function as L increases to infinity. As both K and L approach infinity, this distribution is asymptotically normal. These results are proved by studying the convergence of the characteristic function.
The main result is the asymptotic behavior of P_{K,K}(N) itself, for certain large K and N. This is obtained by studying a contour integral of the generating function taken along the unit circle. The bulk of the estimate comes from integrating along a small arc near the point 1. Diophantine approximation is used to show that the integral along the rest of the circle is much smaller.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  3 May 1965 
Record Number:  CaltechTHESIS:10122015160506112 
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:10122015160506112 
DOI:  10.7907/YH19JH87 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  9215 
Collection:  CaltechTHESIS 
Deposited By:  Leslie Granillo 
Deposited On:  13 Oct 2015 15:06 
Last Modified:  21 Dec 2019 02:25 
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