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＜電子ブック＞
Boolean Representations of Simplicial Complexes and Matroids / by John Rhodes, Pedro V. Silva
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2015.
出版者	Cham : Springer International Publishing : Imprint: Springer
出版年	2015
本文言語	英語
大きさ	X, 173 p. 36 illus : online resource
著者標目	*Rhodes, John author Silva, Pedro V author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Associative rings LCSH:Associative algebras LCSH:Algebraic topology LCSH:Algebraic geometry LCSH:Algebras, Linear LCSH:Discrete mathematics FREE:Order, Lattices, Ordered Algebraic Structures FREE:Associative Rings and Algebras FREE:Algebraic Topology FREE:Algebraic Geometry FREE:Linear Algebra FREE:Discrete Mathematics
一般注記	1. Introduction -- 2. Boolean and superboolean matrices -- 3. Posets and lattices -- 4. Simplicial complexes -- 5. Boolean representations -- 6. Paving simplicial complexes -- 7. Shellability and homotopy type -- 8. Operations on simplicial complexes -- 9. Open questions 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.   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 HTTP:URL=https://doi.org/10.1007/978-3-319-15114-4

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