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An experimental mathematics approach to several combinatorial problems
Descriptive
TitleInfo
Title
An experimental mathematics approach to several combinatorial problems
Name
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NamePart
(type = family)
Yao
NamePart
(type = given)
Yukun
NamePart
(type = date)
1992
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Yao, Yukun, 1992-
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author
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Zeilberger
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Doron
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Doron Zeilberger
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Advisory Committee
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chair
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Kiessling
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Michael
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Michael Kiessling
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Advisory Committee
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internal member
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Retakh
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Vladimir
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Vladimir Retakh
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Advisory Committee
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internal member
Name
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Sloane
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Neil
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Neil Sloane
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Advisory Committee
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outside member
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Rutgers University
Role
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degree grantor
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School of Graduate Studies
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school
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Text
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theses
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2020
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2020-05
Language
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English
Abstract
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Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even automatically prove theorems.
With an experimental mathematics approach, this dissertation deals with several combinatorial problems and demonstrates the methodology of experimental mathematics.
We start with parking functions and their moments of certain statistics. Then we discuss about spanning trees and ``almost diagonal" matrices to illustrate the methodology of experimental mathematics. We also apply experimental mathematics to Quicksort algorithms to study the running time. Finally we talk about the interesting peaceable queens problem.
With an experimental mathematics approach, this dissertation deals with several combinatorial problems and demonstrates the methodology of experimental mathematics.
We start with parking functions and their moments of certain statistics. Then we discuss about spanning trees and ``almost diagonal" matrices to illustrate the methodology of experimental mathematics. We also apply experimental mathematics to Quicksort algorithms to study the running time. Finally we talk about the interesting peaceable queens problem.
Subject
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Topic
Experimental mathematics
Subject
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Topic
Mathematics
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Rutgers University Electronic Theses and Dissertations
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ETD_10636
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1 online resource (vi, 100 pages)
Note
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Ph.D.
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Includes bibliographical references
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
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doi:10.7282/t3-yqpg-yt61
Genre
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ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Yao
GivenName
Yukun
Role
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Permission or license
DateTime
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2020-03-23 15:04:56
AssociatedEntity
Name
Yukun Yao
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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