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Flexible schemes and beyond: experimental enumeration of pattern avoidance classes
Descriptive
TitleInfo
Title
Flexible schemes and beyond: experimental enumeration of pattern avoidance classes
Name
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NamePart
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Biers-Ariel
NamePart
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Yonah
NamePart
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1993
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Biers-Ariel, Yonah, 1993-
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author
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Zeilberger
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Doron
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Doron Zeilberger
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Advisory Committee
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chair
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Kopparty
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Swastik
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Swastik Kopparty
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Advisory Committee
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internal member
Name
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NamePart
(type = family)
Narayanan
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(type = given)
Bhargav
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Bhargav Narayanan
Affiliation
Advisory Committee
Role
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internal member
Name
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Vatter
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Vincent
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Vincent Vatter
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Advisory Committee
Role
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outside member
Name
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Rutgers University
Role
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degree grantor
Name
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NamePart
School of Graduate Studies
Role
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school
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Text
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theses
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2020
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2020-05
Language
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English
Abstract
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This thesis demonstrates several applications of experimental methods to the enumeration of pattern-avoiding permutations. First, we introduce flexible schemes -- a new extension of enumeration schemes. We show how a computer can find flexible schemes and use them to count permutations. We establish sufficient conditions for the existence of finite flexible schemes, and in particular show that they exist whenever finite enumeration schemes or regular insertion encodings do. Next, we combine enumeration schemes with structural arguments to give a new algorithm for counting 1342-avoiding permutations. We find a recurrence for the number of permutations avoiding four dashed patterns, and finally generalize Claude Lenormand's "raboter" sequence. We have implemented all the algorithms described here in Maple and provide links to the Maple code in each section.
Subject
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Topic
Mathematics
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Title
Rutgers University Electronic Theses and Dissertations
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ETD
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Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier
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rucore10001600001
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ETD_10656
Identifier
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doi:10.7282/t3-5fet-n788
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1 online resource (iv, 57 pages)
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Ph.D.
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Includes bibliographical references
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NjNbRU
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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
Biers-Ariel
GivenName
Yonah
Role
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Permission or license
DateTime
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2020-03-27 13:58:31
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Name
Yonah Biers-Ariel
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Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
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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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2020-03-27T13:55:55
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