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An experimental mathematics approach to some combinatorial problems
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Zaleski, Anthony. An experimental mathematics approach to some combinatorial problems. Retrieved from https://doi.org/doi:10.7282/T39W0JZ1

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TitleAn experimental mathematics approach to some combinatorial problems
NameZaleski, Anthony (author); Zeilberger, Doron (chair); Kiessling, Michael (internal member); Retakh, Vladimir (internal member); Sills, Andrew (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-05 (degree)
SubjectMathematics, Experimental mathematics
Extent1 online resource (vii, 76 p. : ill.)
DescriptionWhile 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Anthony Zaleski
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T39W0JZ1
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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