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Boolean representations of simplicial complexes and matroids[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	511.3
書名/作者:	Boolean representations of simplicial complexes and matroids/ by John Rhodes, Pedro V. Silva.
作者:	Rhodes, John.
其他作者:	Silva, Pedro V.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	x, 173 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Algebra, Boolean.
標題:	Boolean matrices.
標題:	Mathematics.
標題:	Order, Lattices, Ordered Algebraic Structures.
標題:	Associative Rings and Algebras.
標題:	Algebraic Topology.
標題:	Algebraic Geometry.
標題:	Linear and Multilinear Algebras, Matrix Theory.
標題:	Combinatorics.
ISBN:	9783319151144 (electronic bk.)
ISBN:	9783319151137 (paper)
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-15114-4

Boolean representations of simplicial complexes and matroids[electronic resource] /
Rhodes, John.

Boolean representations of simplicial complexes and matroids[electronic resource] /by John Rhodes, Pedro V. Silva. - Cham :Springer International Publishing :2015. - x, 173 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

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.

ISBN: 9783319151144 (electronic bk.)

Standard No.: 10.1007/978-3-319-15114-4doiSubjects--Topical Terms:

466351
Algebra, Boolean.

LC Class. No.: QA10.3

Dewey Class. No.: 511.3

Boolean representations of simplicial complexes and matroids[electronic resource] /
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