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Unimodal polynomials and lattice walk enumeration with experimental mathematics
Descriptive
TitleInfo
Title
Unimodal polynomials and lattice walk enumeration with experimental mathematics
Name
(type = personal)
NamePart
(type = family)
Ek
NamePart
(type = given)
Bryan
NamePart
(type = date)
1992-
DisplayForm
Bryan Ek
Role
RoleTerm
(authority = RULIB)
author
Name
(type = personal)
NamePart
(type = family)
Zeilberger
NamePart
(type = given)
Doron
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Doron Zeilberger
Affiliation
Advisory Committee
Role
RoleTerm
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chair
Name
(type = personal)
NamePart
(type = family)
Kopparty
NamePart
(type = given)
Swastik
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Swastik Kopparty
Affiliation
Advisory Committee
Role
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internal member
Name
(type = personal)
NamePart
(type = family)
Saks
NamePart
(type = given)
Michael
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Michael Saks
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Sloane
NamePart
(type = given)
Neil J. A.
DisplayForm
Neil J. A. Sloane
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
School of Graduate Studies
Role
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school
TypeOfResource
Text
Genre
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theses
OriginInfo
DateCreated
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2018
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2018-05
CopyrightDate
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2018
Place
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xx
Language
LanguageTerm
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(type = code)
eng
Abstract
(type = abstract)
The 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.
Subject
(authority = RUETD)
Topic
Mathematics
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
(type = RULIB)
ETD
Identifier
ETD_8880
PhysicalDescription
Form
(authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (ix, 100 p. : ill.)
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Subject
(authority = ETD-LCSH)
Topic
Lattice theory
Note
(type = statement of responsibility)
by Bryan Ek
RelatedItem
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TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier
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rucore10001600001
Location
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T3V1287D
Genre
(authority = ExL-Esploro)
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
Ek
GivenName
Bryan
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2018-04-13 03:22:39
AssociatedEntity
Name
Bryan Ek
Role
Copyright holder
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
RULTechMD
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ETD
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windows xp
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1.5
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2018-04-14T02:54:19
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2018-04-16T15:37:45
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pdfTeX-1.40.11
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