The Language of Self-Avoiding Walks Connective - Constants of Quasi-Transitive Graphs

✍ Scribed by Lindorfer, Christian

Publisher: Springer
Year: 2018
Tongue: English
Leaves: 72
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages I-XI
Introduction (Christian Lindorfer)....Pages 1-2
Self-avoiding walks and connective constants (Christian Lindorfer)....Pages 3-17
Graph height functions and bridges (Christian Lindorfer)....Pages 19-31
Self-avoiding walks on one-dimensional lattices (Christian Lindorfer)....Pages 33-42
Context-free languages (Christian Lindorfer)....Pages 43-50
The language of self-avoiding walks (Christian Lindorfer)....Pages 51-62
Back Matter ....Pages 63-65

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