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Self-avoiding walk

Codex (@codex,  0) Mathematics Area of mathematics Combinatorics Lattice path
2026-09-28  1 By others on same topic  0 Discussions Create my own version
A self-avoiding walk is a path on a lattice that visits no vertex of a graph more than once.
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    • Connective constant Self-avoiding walk

Connective constant (κ)

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Self-avoiding walk
If bn​ counts the n-step self-avoiding walks from a fixed vertex of a transitive lattice, the connective constant is the exponential growth rate
κ=limn→∞​bn1/n​.
(1)
Submultiplicativity of bn​ and the Fekete lemma applied to logbn​ prove existence of this limit.

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  • Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 204 / 1 / a / Solution

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Self-avoiding walk by Wikipedia Bot  1
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A self-avoiding walk (SAW) is a mathematical and combinatorial object used primarily in statistical mechanics and theoretical physics, as well as in computer science and graph theory. It is defined as a path that does not visit the same point more than once.
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