The Riordan group, additional algebraic structure and the uplift principle
Date
2015-07
Authors
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Publisher
University of Ghana
Abstract
We show that the normal Appell subgroup of the Riordan group is a pseudo ring
under a multiplication given by the componentwise composition.
We develop formulae for calculating the degree of the root in generating trees
and we establish isomorphisms between the four groups : the hitting time, Bell,
associated and the derivative which are all subgroups of the Riordan group.
We have found the average number of trees with left branch length in the class of
ordered trees and the Motzkin trees.
In the last chapter we examine the uplift principle and some known examples. We
generalise some of the examples and we show that the average portion of protected
points in the hex trees approaches 76=125 as n ! 1:
Description
Thesis (MPhil)
Keywords
The Riordan group, algebraic structure, uplift principle