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Enumeration schemes for pattern-avoiding words and permutations
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Title
Enumeration schemes for pattern-avoiding words and permutations
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Pudwell
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Lara Kristin
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Lara Kristin Pudwell
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author
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Zeilberger
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Doron
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Advisory Committee
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Doron Zeilberger
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chair
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Beck
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Jozsef
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Advisory Committee
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Jozsef Beck
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Retakh
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Vladimir
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Advisory Committee
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Vladimir Retakh
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internal member
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Sloane
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Neil
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Advisory Committee
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Neil Sloane
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Rutgers University
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Graduate School - New Brunswick
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theses
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2008
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2008-05
Language
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English
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electronic
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ix, 110 pages
Abstract
Let p=p_1...p_n and q=q_1...q_m be permutations. We say that p contains q as a pattern if there are indices 1 [less than]= i_1 [less than] ... [less than] i_m [less than]= n such that p_{i_j} [less than] p_{i_k} if and only if q_i [less than] q_k; otherwise, p avoids q. The study of pattern avoidance in permutations is well studied from a variety of perspectives. This thesis is concerned with two generalizations of this pattern avoidance problem. The first generalization is that of pattern avoidance in words (where p and q may have repeated letters). The second is that of barred permutation patterns (where p avoids q unless q is part of an instance of an even larger pattern in p). In both cases, we seek to find universal methods that count words (resp. permutations) avoiding a particular set of patterns, and automate these methods to achieve new enumeration results.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 107-109).
Subject
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Topic
Mathematics
Subject
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Topic
Permutations
Subject
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Topic
Mathematics
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17374
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ETD_844
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Identifier
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doi:10.7282/T3474B63
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ETD doctoral
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Lara Pudwell
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Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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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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