04680nam 22008775 450 991029978010332120200702152649.03-319-15114-210.1007/978-3-319-15114-4(CKB)3710000000360309(EBL)1998165(OCoLC)904248939(SSID)ssj0001452145(PQKBManifestationID)11759885(PQKBTitleCode)TC0001452145(PQKBWorkID)11479117(PQKB)10469119(DE-He213)978-3-319-15114-4(MiAaPQ)EBC1998165(PPN)184497930(EXLCZ)99371000000036030920150226d2015 u| 0engur|n|---|||||txtccrBoolean Representations of Simplicial Complexes and Matroids[electronic resource] /by John Rhodes, Pedro V. Silva1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (179 p.)Springer Monographs in Mathematics,1439-7382Description based upon print version of record.3-319-15113-4 Includes bibliographical references at the end of each chapters and indexes.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.Springer Monographs in Mathematics,1439-7382AlgebraOrdered algebraic structuresAssociative ringsRings (Algebra)Algebraic topologyAlgebraic geometryMatrix theoryCombinatoricsOrder, Lattices, Ordered Algebraic Structureshttps://scigraph.springernature.com/ontologies/product-market-codes/M11124Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Algebra.Ordered algebraic structures.Associative rings.Rings (Algebra).Algebraic topology.Algebraic geometry.Matrix theory.Combinatorics.Order, Lattices, Ordered Algebraic Structures.Associative Rings and Algebras.Algebraic Topology.Algebraic Geometry.Linear and Multilinear Algebras, Matrix Theory.Combinatorics.511.324Rhodes Johnauthttp://id.loc.gov/vocabulary/relators/aut345558Silva Pedro Vauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299780103321Boolean Representations of Simplicial Complexes and Matroids2540391UNINA