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Boolean Representations of Simplicial Complexes and Matroids

Buch | Hardcover
X, 173 Seiten
2015 | 2015
Springer International Publishing (Verlag)
978-3-319-15113-7 (ISBN)

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

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.

Erscheint lt. Verlag 24.3.2015
Reihe/Serie Springer Monographs in Mathematics
Zusatzinfo X, 173 p. 36 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 444 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte Boolean Matrix • combinatorics • Lattice Representations • matrix theory • Posets • Representation Theory • shellability and homotopy type • Simplicial Complexes
ISBN-10 3-319-15113-4 / 3319151134
ISBN-13 978-3-319-15113-7 / 9783319151137
Zustand Neuware
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