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作者 Drake, Brian
書名 An inversion theorem for labeled trees and some limits of areas under lattice paths
國際標準書號 9780549699262
book jacket
說明 114 p
附註 Source: Dissertation Abstracts International, Volume: 69-08, 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 ex--1 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 q-Catalan numbers approach a limit coefficientwise. This follows from the interpretation of their q-Catalan numbers as counting the area between certain lattice paths and the x-axis. We consider other well-known 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
Host Item Dissertation Abstracts International 69-08B
主題 Mathematics
Alt Author Brandeis University. Mathematics
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