CC BY-SA 4.0 UnportedDuminil-Copin, Hugo2022-08-052022-08-052019https://oa.tib.eu/renate/handle/123456789/9909http://dx.doi.org/10.34657/8947In 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.enghttps://creativecommons.org/licenses/by-sa/4.0/510Probability Theory and StatisticsReport11 S.