New upper bound for the connective constant for square-lattice self-avoiding walks

2022/11/29 by Olivier Couronné, Couronné, Olivier · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · doi:10.48550/arxiv.2211.16146

openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By modifying the automaton used by Pönitz and Tittman [4], and considering loops of length up to 26, we obtain 2.662343 as an upper bound for the connective constant in the lattice Z 2 .

Cited by

• Existence and bounds of growth constants for restricted walks, surfaces, and generalisations

Related

• Upper bounds for the connective constant of weighted self-avoiding walks
• Self-avoiding Walks of Lattice Strips
• Lectures on Self-Avoiding Walks
• The connective constant of the honeycomb lattice equals\n \√(2+\√2)
• Counting self-avoiding walks