# Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices

@article{Guttmann2022SelfavoidingWA, title={Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices}, author={Anthony J. Guttmann and Iwan Jensen}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2022}, volume={55} }

We have analysed the recently extended series for the number of self-avoiding walks (SAWs) CL(1) that cross an L × L square between diagonally opposed corners. The number of such walks is known to grow as λSL2. We have made more precise the estimate of λS, based on additional series coefficients provided by several authors, and refined analysis techniques. We estimate that λS=1.7445498±0.0000012. We have also studied the subdominant behaviour, and conjecture that CL(1)∼λSL2+bL+c⋅Lg, where b=−0…

## 3 Citations

### Self-avoiding walks contained within a square

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

We have studied self-avoiding walks contained within an L × L square whose end-points can lie anywhere within, or on, the boundaries of the square. We prove that such walks behave, asymptotically, as…

### The scaling limit of the weakly self-avoiding walk on a high-dimensional torus

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- 2021

How long does a self-avoiding walk on a discrete d -dimensional torus have to be before it begins to behave diﬀerently from a self-avoiding walk on Z d ? We consider a version of this question for…

### C O ] 2 6 N ov 2 02 2 The gerrymander sequence , or A 348456

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- 2022

Recently Kauers, Koutschan and Spahn announced a significant increase in the length of the so-called gerrymander sequence, given as A348456 in the OEIS, extending the sequence from 3 terms to 7…

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