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Automated discovery and proof in three combinatorial problems

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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Automated discovery and proof in three combinatorial problems
SubTitle
PartName
PartNumber
NonSort
Identifier (displayLabel = ); (invalid = )
ETD_2062
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051892
Language (objectPart = )
LanguageTerm (authority = ISO639-2); (type = code)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Combinatorial analysis
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Graph theory
Abstract
In this Ph.D. disseration, I will go over advances I have made in three combinatorial problems. The running theme throughout these three problems is the novel use of computers to aid not only in the discovery of the theorems proved, but also in the proofs themselves. The first problem concerns the quantity f_D(n), defined as the size of the largest subset of [n] avoiding differences in D. Originally motivated by the Triangle Conjecture of Schutzenberger and Perrin, we again define an enumeration scheme that will find, and prove automatically, the sequence {f_D(n)} from 1 to infinity for any prescribed D. Although the Triangle Conjecture has long been refuted, we present an asymptotic version of it and prove it. The second problem involves the enumeration of spanning trees in grid graphs – graphs of the form G x P_n (or C_n) for arbitrary G. An enumeration scheme is developed based on the partitions of [n], yielding an algorithmic method to completely solve the sequence for any G. These techniques yield a surprising consequence: sequences obtained in this manner are divisibility sequences. The
final problem is the firefighter problem, a dynamic graph theory problem modeling the spread of diseases, information, etc. We will present the problem as it applies on the two-dimensional grid and prove new upper and lower bounds, found mainly through computer experimentation.
PhysicalDescription
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electronic resource
Extent
x, 118 p. : ill.
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application/pdf
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 114-117)
Note (type = statement of responsibility)
by Paul Raff
Name (ID = NAME-1); (type = personal)
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Raff
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Paul
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1982-
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author
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Paul Raff
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Zeilberger
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Doron
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chair
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Advisory Committee
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Doron Zeilberger
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Roberts
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Fred
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internal member
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Advisory Committee
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Fred Roberts
Name (ID = NAME-4); (type = personal)
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Retakh
NamePart (type = given)
Vladimir
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internal member
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Advisory Committee
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Vladimir Retakh
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Sloane
NamePart (type = given)
Neil
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outside member
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Advisory Committee
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Neil Sloane
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
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degree grantor
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NamePart
Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-10
Place
PlaceTerm (type = code)
xx
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3T72HM0
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work
Copyright
Status
Copyright protected
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Raff
GivenName
Paul
Role
Copyright holder
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Permission or license
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Place
DateTime
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Name
Paul Raff
Affiliation
Rutgers University. Graduate School - New Brunswick
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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.
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Technical

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ETD
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application/pdf
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application/x-tar
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778240
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