Counting self-avoiding walks on the hexagonal lattice

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Counting self-avoiding walks on the hexagonal lattice

In how many ways can you go for a walk along a lattice grid in such a way that you never meet your own trail? In this snapshot, we describe some combinatorial and statistical aspects of these so-called self-avoiding walks. In particular, we discuss a recent result concerning the number of self-avoiding walks on the hexagonal (“honeycomb”) lattice. In the last part, we briefly hint at the connection to the geometry of long random self-avoiding walks.

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Mathematical subjects

Probability Theory and Statistics


Hugo Duminil-Copin


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Algebra and Number Theory
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Discrete Mathematics and Foundations
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