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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 ...

Consider a Cayley graph of some big finite group. Consider random walk on such a graph - think of it as drunk driver. Fix some number $N$ which is much smaller than group size. Question 1: How to ...

Context: Algorithms to find short paths on Cayley graphs of (finite) groups are of some interest - see below. There can be several approaches to that task. One of ideas coming to my mind - in some ...

We can look on the permutohedron as a kind of "embedding" of the Cayley graph of $S_n$ to the Euclidean space. (That Cayley graph is constructed by the standard generators, i.e. ...

The Permutohedron is a remarkable convex polytope in $R^n$, such that its nodes are indexed by permutations and edges correspond to the Cayley graph of $S_n$ with respect to the standard generators, i....

Question: I wonder what are the open problems , where computational experiments might me helpful? (Setting some bounds, excluding some cases, shaping some expectations ). Grant program: The context of ...