Boolean Representations of Simplicial Complexes and Matroids / / by John Rhodes, Pedro V. Silva

• Record Nr.: UNINA9910299780103321
• Autore: Rhodes John
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• ISBN: 3-319-15114-2
• Edizione: [1st ed. 2015.]
• Descrizione fisica: 1 online resource (179 p.)
• Collana: Springer Monographs in Mathematics, , 1439-7382
• Disciplina: 511.324
• Soggetti: Algebra; Ordered algebraic structures; Associative rings; Rings (Algebra); Algebraic topology; Geometry, Algebraic; Matrix theory; Combinatorial analysis; Order, Lattices, Ordered Algebraic Structures; Associative Rings and Algebras; Algebraic Topology; Algebraic Geometry; Linear and Multilinear Algebras, Matrix Theory; Combinatorics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and indexes.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.