The combinatorics of adinkras
Name
867870369-MIT.pdf
Description
Full printable version
Size
4.62 MB
Format
Adobe PDF
Checksum (MD5)
2388121da9147a6f0e265ceed182d966
Author(s)
Zhang, Yan, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Richard Stanley.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
Abstract
Adinkras are graphical tools created to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems of algebraic, combinatorial, and computational nature. In this work, we make a self-contained treatment of the mathematical foundations of adinkras that slightly generalizes the existing literature. Then, we make new connections to other areas including homological algebra, theory of polytopes, Pfaffian orientations, graph coloring, and poset theory. Selected results include the enumeration of odd dashings for all adinkraizable chromotopologies, the notion of Stiefel-Whitney classes for codes and their vanishing conditions, and the enumeration of all Hamming cube adinkras up through dimension 5.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 67-69).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
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