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Unimodal polynomials and lattice walk enumeration with experimental mathematics
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Ek, Bryan. Unimodal polynomials and lattice walk enumeration with experimental mathematics. Retrieved from https://doi.org/doi:10.7282/T3V1287D

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TitleUnimodal polynomials and lattice walk enumeration with experimental mathematics
NameEk, Bryan (author); Zeilberger, Doron (chair); Kopparty, Swastik (internal member); Saks, Michael (internal member); Sloane, Neil J. A. (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-05 (degree)
SubjectMathematics, Lattice theory
Extent1 online resource (ix, 100 p. : ill.)
DescriptionThe main theme of this dissertation is retooling methods to work for different situations. I have taken the method derived by O'Hara and simplified by Zeilberger to prove unimodality of q-binomials and tweaked it. This allows us to create many more families of polynomials for which unimodality is not, a priori, given. I analyze how many of the tweaks affect the resulting polynomial. Ayyer and Zeilberger proved a result about bounded lattice walks. I employ their generating function relation technique to analyze lattice walks with a general step set in bounded, semi-bounded, and unbounded planes. The method in which we do this is formulated to be highly algorithmic so that a computer can automate most, if not all, of the work. I easily recover many well-known results for simpler step sets and discover new results for more complex step sets.
NotePh.D.
NoteIncludes bibliographical references
Noteby Bryan Ek
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3V1287D
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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