Overview
- Contains open problems and new ideas for research
- Develops a geometric theory in an extended context
- Uses the lattice structure for all representations of boolean representations of simplicial complexes
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (9 chapters)
Keywords
About this book
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context.
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Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.
Authors and Affiliations
Bibliographic Information
Book Title: Boolean Representations of Simplicial Complexes and Matroids
Authors: John Rhodes, Pedro V. Silva
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-15114-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-15113-7Published: 24 March 2015
Softcover ISBN: 978-3-319-38367-5Published: 09 October 2016
eBook ISBN: 978-3-319-15114-4Published: 26 February 2015
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: X, 173
Number of Illustrations: 36 b/w illustrations
Topics: Order, Lattices, Ordered Algebraic Structures, Associative Rings and Algebras, Algebraic Topology, Algebraic Geometry, Linear and Multilinear Algebras, Matrix Theory, Combinatorics