說明 
114 p 
附註 
Source: Dissertation Abstracts International, Volume: 6908, Section: B, page: 

Adviser: Ira Gessel 

Thesis (Ph.D.)Brandeis University, 2008 

The main result of this work is a combinatorial interpretation of the inversion of exponential generating functions. The simplest example is an explanation of the fact that ex1 and log(1+x) are compositional inverses. The combinatorial interpretation is based on building labeled trees out of building blocks using certain combining rules. Using a subset of the rules leads to trees counted by one exponential generating function, while the complementary set of rules leads to the inverse function. We apply this inversion theorem to a variety of problems in the enumeration of labeled trees and related combinatorial objects 

We also study a problem in lattice path enumeration. Carlitz and Riordan [10] showed that reversed qCatalan numbers approach a limit coefficientwise. This follows from the interpretation of their qCatalan numbers as counting the area between certain lattice paths and the xaxis. We consider other wellknown families of lattice paths and find the analogous limits. For some families, the limits are interpreted as counting restricted integer partitions, while others count generalized Frobenius partitions and related arrays 

School code: 0021 

DDC 
Host Item 
Dissertation Abstracts International 6908B

主題 
Mathematics


0405

Alt Author 
Brandeis University. Mathematics

