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Boolean Representations of Simplicial Complexes and Matroids

  • John Rhodes
  • Pedro V. Silva

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. John Rhodes, Pedro V. Silva
    Pages 1-8
  3. John Rhodes, Pedro V. Silva
    Pages 9-15
  4. John Rhodes, Pedro V. Silva
    Pages 17-30
  5. John Rhodes, Pedro V. Silva
    Pages 31-37
  6. John Rhodes, Pedro V. Silva
    Pages 39-83
  7. John Rhodes, Pedro V. Silva
    Pages 85-103
  8. John Rhodes, Pedro V. Silva
    Pages 105-122
  9. John Rhodes, Pedro V. Silva
    Pages 123-138
  10. John Rhodes, Pedro V. Silva
    Pages 139-142
  11. Back Matter
    Pages 143-173

About this book

Introduction

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.

Keywords

Boolean Matrix Lattice Representations Posets representation theory shellability and homotopy type simplicial complexes

Authors and affiliations

  • John Rhodes
    • 1
  • Pedro V. Silva
    • 2
  1. 1.University of California, Berkeley Dept. MathematicsBerkeleyUSA
  2. 2.Department of MathematicsUniversity of PortoPortoPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15114-4
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-15113-7
  • Online ISBN 978-3-319-15114-4
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site