RUcore Resource Object
RUcore Resource Object
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Uniform TitleEnumeration schemes for pattern-avoiding words and permutations
NamePudwell, Lara Kristin (author), Zeilberger, Doron (chair), Beck, Jozsef (internal member), Retakh, Vladimir (internal member), Sloane, Neil (outside member), Rutgers University, Graduate School - New Brunswick,
Degree Date2008-05
Date Created2008
SubjectMathematics,
Permutations,
Mathematics
DescriptionLet 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.
NotePh.D.
NoteIncludes bibliographical references (p. 107-109).
Genretheses
Persistent URLhttp://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17374
LanguageEnglish
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.