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An experimental mathematics approach to some combinatorial problems
Descriptive
TitleInfo
Title
An experimental mathematics approach to some combinatorial problems
Name
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NamePart
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Zaleski
NamePart
(type = given)
Anthony
NamePart
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1994-
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Anthony Zaleski
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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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Sills
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Andrew
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Andrew Sills
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Advisory Committee
Role
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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
Role
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school
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Text
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theses
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2018
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2018-05
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2018
Place
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xx
Language
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eng
Abstract
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While computers have long been used for numeric computations, their growing power to handle symbolic manipulations is becoming increasingly useful in mathematics. Our "experimental mathematics" approach uses symbolic computing as an essential tool to both conjecture and prove new results, often with little or no human intervention. Here, we will illustrate how we used experimental mathematics to explore several combinatorial problems. Namely, we will start out with a brief analysis of the generating functions of some statistics associated with random walks in the plane. Then, we will do the same for certain families of simultaneous core integer partitions; this constitutes the bulk of the thesis and contains our main results. We will briefly cover our attempts to apply computer implementations of inclusion-exclusion to Ramsey theory and Boolean satisfiability. Finally, we will introduce a Boolean analog of Erdos' integer covering systems and go over some related results and conjectures.
Subject
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Topic
Mathematics
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_8755
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (vii, 76 p. : ill.)
Note
(type = degree)
Ph.D.
Note
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Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Experimental mathematics
Note
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by Anthony Zaleski
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Title
School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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NjNbRU
Identifier
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doi:10.7282/T39W0JZ1
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
Zaleski
GivenName
Anthony
Role
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RightsEvent
Type
Permission or license
DateTime
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2018-04-04 19:37:37
AssociatedEntity
Name
Anthony Zaleski
Role
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Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
License
Name
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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Technical
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2018-04-04T19:24:47
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2018-04-04T19:24:47
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