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Richard P. Stanley. Klivans, Caroline J. (Caroline Jane), 1977- Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Department of Mathematics 2005-10-14T20:03:42Z 2005-10-14T20:03:42Z 2003 2003 http://hdl.handle.net/1721.1/29358 52769866 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003. Includes bibliographical references (p. 61-62). In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face with a node of smaller label results in a collection which is also a face. A primary motivation for considering shifted complexes is a procedure called shifting. Shifting associates a shifted complex to any simplicial complex in a way which preserves meaningful information, while simplifying the structure of the complex. For example, shifting preserves the f-vector of a complex but always reduces the topology to a wedge of spheres. Shifting has proved to be a successful tool for answering questions regarding f-vectors. While most of the previous results on shifted complexes are algebraic or topological in nature, we explore the combinatorics of shifted complexes. We give intrinsic characterization theorems for shifted complexes and shifted matroid complexes. In addition, we show results on the enumeration of shifted complexes and connections to various combinatorial structures. by Caroline J. Klivans. Ph.D. 62 p. 1972159 bytes 1971968 bytes application/pdf application/pdf eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Mathematics. Combinatorial properties of shifted complexes Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="56860e2b-f0d3-4f74-9109-b8e526a88f10"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Combinatorial properties of shifted complexes</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2003</PublicationDate> <Authors> <Author> <DisplayName>Klivans, Caroline J. (Caroline Jane), 1977-</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Mathematics.</Keyword> <Abstract>In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face with a node of smaller label results in a collection which is also a face. A primary motivation for considering shifted complexes is a procedure called shifting. Shifting associates a shifted complex to any simplicial complex in a way which preserves meaningful information, while simplifying the structure of the complex. For example, shifting preserves the f-vector of a complex but always reduces the topology to a wedge of spheres. Shifting has proved to be a successful tool for answering questions regarding f-vectors. While most of the previous results on shifted complexes are algebraic or topological in nature, we explore the combinatorics of shifted complexes. We give intrinsic characterization theorems for shifted complexes and shifted matroid complexes. In addition, we show results on the enumeration of shifted complexes and connections to various combinatorial structures.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>