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Universal labeling algebras as invariants of layered graphs

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TitleInfo
Title
Universal labeling algebras as invariants of layered graphs
Name (type = personal)
NamePart (type = family)
Durst
NamePart (type = given)
Susan
NamePart (type = date)
1985-
DisplayForm
Susan Durst
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Wilson
NamePart (type = given)
Robert Lee
DisplayForm
Robert Lee Wilson
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Retakh
NamePart (type = given)
Vladimir
DisplayForm
Vladimir Retakh
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Lepowsky
NamePart (type = given)
James
DisplayForm
James Lepowsky
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Nacin
NamePart (type = given)
David
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David Nacin
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2013
DateOther (qualifier = exact); (type = degree)
2013-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract
In this work we will study the universal labeling algebra A(Γ), a related algebra B(Γ), and their behavior as invariants of layered graphs. We will introduce the notion of an upper vertex-like basis, which allows us to recover structural information about the graph Γ from the algebra B(Γ). We will use these bases to show that several classes of layered graphs are uniquely identifi ed by their corresponding algebras B(Γ). We will use the same techniques to construct large classes of nonisomorphic graphs with isomorphic B(Γ). We will also explore the graded structure of the algebra A(Γ), using techniques developed by C. Duff y, I. Gelfand, V. Retakh, S. Serconek and R. Wilson to find formulas for the Hilbert series and graded trace generating functions of A(Γ) when is the Hasse diagram of a direct product of partially ordered sets.
Subject (authority = RUETD)
Topic
Mathematics
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4645
PhysicalDescription
Form (authority = gmd)
electronic resource
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application/pdf
InternetMediaType
text/xml
Extent
iv, 81 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Susan Durst
Subject (authority = ETD-LCSH)
Topic
Mathematics--Charts, diagrams, etc.
Subject (authority = ETD-LCSH)
Topic
Algebra, Universal
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068846
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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/T3J964ZN
Genre (authority = ExL-Esploro)
ETD doctoral
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RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Durst
GivenName
Susan
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2013-04-12 00:18:58
AssociatedEntity
Name
Susan Durst
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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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ETD
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windows xp
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