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© 2018

The Language of Self-Avoiding Walks

Connective Constants of Quasi-Transitive Graphs

Book

Part of the BestMasters book series (BEST)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Christian Lindorfer
    Pages 1-2
  3. Christian Lindorfer
    Pages 3-17
  4. Christian Lindorfer
    Pages 19-31
  5. Christian Lindorfer
    Pages 33-42
  6. Christian Lindorfer
    Pages 43-50
  7. Christian Lindorfer
    Pages 51-62
  8. Back Matter
    Pages 63-65

About this book

Introduction

The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees.

Contents

  • Graph Height Functions and Bridges
  • Self-Avoiding Walks on One-Dimensional Lattices
  • The Algebraic Theory of Context-Free Languages
  • The Language of Walks on Edge-Labelled Graphs

Target Groups

  • Researchers and students in the fields of graph theory, formal language theory and combinatorics
  • Experts in these areas

The Author
Christian Lindorfer wrote his master’s thesis under the supervision of Prof. Dr. Wolfgang Woess at the Institute of Discrete Mathematics at Graz University of Technology, Austria.

Keywords

Self-avoiding walks Context-free languages Edge-labelld graphs Graph height functions Bridges k-ladder-tree One-dimensional lattices

Authors and affiliations

  1. 1.GrazAustria

About the authors

Christian Lindorfer wrote his master’s thesis under the supervision of Prof. Dr. Wolfgang Woess at the Institute of Discrete Mathematics at Graz University of Technology, Austria.

Bibliographic information

  • Book Title The Language of Self-Avoiding Walks
  • Book Subtitle Connective Constants of Quasi-Transitive Graphs
  • Authors Christian Lindorfer
  • Series Title BestMasters
  • Series Abbreviated Title BestMasters
  • DOI https://doi.org/10.1007/978-3-658-24764-5
  • Copyright Information Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2018
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-658-24763-8
  • eBook ISBN 978-3-658-24764-5
  • Series ISSN 2625-3577
  • Series E-ISSN 2625-3615
  • Edition Number 1
  • Number of Pages XI, 65
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
    Computational Mathematics and Numerical Analysis
    Geometry
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