Combinatorial properties of shifted complexes
Name
52769866-MIT.pdf
Description
Full printable version
Size
1.88 MB
Format
Adobe PDF
Checksum (MD5)
baeac557d7e1c487a0daa50bf3a6356d
Author(s)
Klivans, Caroline J. (Caroline Jane), 1977-
Advisor(s)
Richard P. Stanley.
Date Issued
2003
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 61-62).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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