Home
Resource
Flexible schemes and beyond: experimental enumeration of pattern avoidance classes
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(335.23 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Biers-Ariel, Yonah. Flexible schemes and beyond: experimental enumeration of pattern avoidance classes. Retrieved from https://doi.org/doi:10.7282/t3-5fet-n788

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleFlexible schemes and beyond: experimental enumeration of pattern avoidance classes
NameBiers-Ariel, Yonah (author); Zeilberger, Doron (chair); Kopparty, Swastik (internal member); Narayanan, Bhargav (internal member); Vatter, Vincent (outside member); Rutgers University; School of Graduate Studies
Date Created2020
Other Date2020-05 (degree)
SubjectMathematics
Extent1 online resource (iv, 57 pages)
DescriptionThis 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.
NotePh.D.
NoteIncludes bibliographical references
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-5fet-n788
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024