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Experimental methods applied to the computation of integer sequences
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TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Experimental methods applied to the computation of integer sequences
Identifier
ETD_1686
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051398
Language
LanguageTerm (authority = ISO639-2)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Number theory
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Combinatorial analysis
Abstract
We apply techniques of experimental mathematics to certain problems in number theory and combinatorics. The goal in each case is to understand certain integer sequences, where foremost we are interested in computing a sequence faster than by its definition. Often this means taking a sequence of integers that is defined recursively and rewriting it without recursion as much as possible. The benefits of doing this are twofold. From the view of computational complexity, one obtains an algorithm for computing the system that is faster than the original; from the mathematical view, one obtains new information about the structure of the system.
Two particular topics are studied with the experimental method. The first is the recurrence a(n) = a(n - 1) + gcd(n, a(n - 1)), which is shown to generate primes in a certain sense. The second is the enumeration of binary trees avoiding a given pattern and extensions of this problem. In each of these problems, computing sequences quickly is intimately connected to understanding the structure of the objects and being able to prove theorems about them.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
vii, 60 p. : ill.
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application/pdf
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text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 57-59)
Note (type = statement of responsibility)
by Eric Samuel Rowland
Name (ID = NAME-1); (type = personal)
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Rowland
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Eric Samuel
NamePart (type = date)
1982
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author
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Eric Samuel Rowland
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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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Bumby
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Richard
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internal member
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Advisory Committee
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Richard Bumby
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Greenfield
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Stephen
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internal member
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Advisory Committee
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Stephen Greenfield
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
RoleTerm (authority = RULIB); (type = )
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-05
Place
PlaceTerm (type = code)
xx
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3T72HPW
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
Availability
Status
Open
RightsEvent (AUTHORITY = rulib); (ID = 1)
Type
Permission or license
Detail
Non-exclusive ETD license
AssociatedObject (AUTHORITY = rulib); (ID = 1)
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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808960
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