Boolean Representations of Simplicial Complexes and Matroids

• Main Authors: Rhodes, John (Author), Silva, Pedro V. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebraic geometry.; Associative rings.; Rings (Algebra).; Matrix theory.; Algebra.; Ordered algebraic structures.; Algebraic topology.; Combinatorics.; Order, Lattices, Ordered Algebraic Structures.; Associative Rings and Algebras.; Algebraic Topology.; Algebraic Geometry.; Linear and Multilinear Algebras, Matrix Theory.

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 importa...

Table of Contents:

• 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.