LEADER 04680nam 22008775 450 001 9910299780103321 005 20200702152649.0 010 $a3-319-15114-2 024 7 $a10.1007/978-3-319-15114-4 035 $a(CKB)3710000000360309 035 $a(EBL)1998165 035 $a(OCoLC)904248939 035 $a(SSID)ssj0001452145 035 $a(PQKBManifestationID)11759885 035 $a(PQKBTitleCode)TC0001452145 035 $a(PQKBWorkID)11479117 035 $a(PQKB)10469119 035 $a(DE-He213)978-3-319-15114-4 035 $a(MiAaPQ)EBC1998165 035 $a(PPN)184497930 035 $a(EXLCZ)993710000000360309 100 $a20150226d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBoolean Representations of Simplicial Complexes and Matroids$b[electronic resource] /$fby John Rhodes, Pedro V. Silva 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (179 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-319-15113-4 320 $aIncludes bibliographical references at the end of each chapters and indexes. 327 $a1. 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. 330 $aThis self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context.   Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aAssociative rings 606 $aRings (Algebra) 606 $aAlgebraic topology 606 $aAlgebraic geometry 606 $aMatrix theory 606 $aCombinatorics 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aAlgebraic topology. 615 0$aAlgebraic geometry. 615 0$aMatrix theory. 615 0$aCombinatorics. 615 14$aOrder, Lattices, Ordered Algebraic Structures. 615 24$aAssociative Rings and Algebras. 615 24$aAlgebraic Topology. 615 24$aAlgebraic Geometry. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aCombinatorics. 676 $a511.324 700 $aRhodes$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$0345558 702 $aSilva$b Pedro V$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299780103321 996 $aBoolean Representations of Simplicial Complexes and Matroids$92540391 997 $aUNINA