• Corpus ID: 222341581

Self-avoiding walks and multiple context-free languages

  title={Self-avoiding walks and multiple context-free languages},
  author={Florian Lehner and Christian Lindorfer},
Let $G$ be a quasi-transitive, locally finite, connected graph rooted at a vertex $o$, and let $c_n(o)$ be the number of self-avoiding walks of length $n$ on $G$ starting at $o$. We show that if $G$ has only thin ends, then the generating function $F_{\mathrm{SAW},o}(z)=\sum_{n \geq 0} c_n(o) z^n$ is an algebraic function. In particular, the connective constant of such a graph is an algebraic number. If $G$ is deterministically edge labelled, that is, every (directed) edge carries a label such… 

Self‐avoiding walk on the hypercube

  • G. Slade
  • Mathematics
    Random Structures & Algorithms
  • 2022
The counting of self-avoiding walks is a classical problem in enumerative combinatorics which is also of interest in probability theory, statistical physics, and polymer chemistry. We study the

Technical Report Column

This report presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually cataloging and cataloging all the components of a smart phone.

Self-avoiding walks and polygons on hyperbolic graphs

We prove that for the $d$-regular tessellations of the hyperbolic plane by $k$-gons, there are exponentially more self-avoiding walks of length $n$ than there are self-avoiding polygons of length



Cutting up graphs

It is shown that there is a subsetd ⊂V Γ which has the following properties: bothd andd*=VΓ\d are infinite.

S-functions for graphs

S-functions are mappings from the class of finite graphs into the set of integers, such that certain formal conditions are fulfilled which are shared by the chromatic number, the vertex-connectivity,

Vertex-Transitive Graphs and Accessibility

It is proved that every locally finite, vertex-transitive graph with at least one thick end has a thick end with a 2-way infinite geodesic, while no thin end hasA 2- way infinite geode, and those ends in a local finite, accessible vertex- transitive graph are precisely the thick ends.

Multiple Context-Free Grammars

It is outlined that the expressivity of m-MCFG’s increases with the parameter m and that the class of tree-adjoining languages is properly included in theclass of 2-multiple context-free languages.

The Language of Self-Avoiding Walks

This work characterize under which conditions on the graph structure this language is regular or context-free: if and only if the graph has more than one end, and the size of all ends is 1, or at most 2, respectively.

Comparing consecutive letter counts in multiple context-free languages

Automorphisms and endomorphisms of infinite locally finite graphs

Random self-avoiding walks on one-dimensional lattices

For a general class of one-dimensional lattices, we show that the generating function for self-avoiding walks can be explicitly expressed in terms of a generating matrix. Further, the connective

Self-avoiding walks

Über die Maximalzahl fremder unendlicher Wege in Graphen