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On the cogrowth series of free products of finite groups

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2021-04-19
Authors/Contributors
Abstract
Given a group G with a finite set of generators, S, it is natural to ask if the product of n generators from S evaluate to the identity. The enumerative version of this problem, known as the cogrowth problem, counts the number of such products and studies the associated counting sequence. Many cogrowth sequences are known. This thesis focuses on the free products of finite groups: Specifically, cyclic and dihedral groups. Such groups have the property that their cogrowth generating functions are algebraic functions, and thus, are solutions to implicit polynomial equations. Using algebraic elimination techniques and free probability theory, we establish upper bounds on the degrees of the polynomial equations that they satisfy. This has implications for asymptotic enumeration, and makes it theoretically possible to determine the functions explicitly.
Document
Identifier
etd21315
Copyright statement
Copyright is held by the author(s).
Permissions
This thesis may be printed or downloaded for non-commercial research and scholarly purposes.
Supervisor or Senior Supervisor
Thesis advisor: Mishna, Marni
Language
English
Member of collection
Download file Size
input_data\21287\etd21315.pdf 5.53 MB

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