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Standard setup. Consider a group and choose generators. Word-metric (or in the other words - distance on the Cayley graph of the group+generators) - converts a group into a metric space, which is ...

Take a standard finite Heisenberg group with two standard generators and let's consider its growth polynomial - the polynomial which coefficients are equal to the sphere sizes. For example for $H_3(Z/...

Looking on the growth function for Rubik's group and symmetric group, one sees rather different behaviour: Rubik's growth in LOG scale (see MO322877): S_n n=9 growth and nice fit by normal ...

Consider finite group $G$ , symmetric set of its elements $S$, construct a Cayley graph. Consider $d(g)$ - word metric or distance on the Cayley graph from identity to $g$. As any function on a group ...

This is a very general question: are there known examples of Ramanujan behaviour of Cayley graphs obtained from family of finite p-groups? ${\mathrm{\bf Adjacency~matrix:}}$ Given a graph ${\mathcal{G}...

Let $G$ be a perfect/ weakly perfect Cayley graph on an abelian group with respect to a symmetric generating set. In addition let the clique number be $\omega$ which divides the order of graph $n$. ...