**Problem of the Week**

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**Hilton Memorial Lecture**

seminars:comb:abstract.201110bid

Let G be a finitely generated group with minimal generating set of size d. For each t ≥ d let Γ_{t} = Γ_{t}(G) be the graph with vertex set V consisting of all generating t-tuples of elements of G and with edges ^{1)} if for some distinct i and j, g'_{i} is g_{i} multiplied on left or right by g_{j}^{±1}, and all other g'_{k} are the same as the corresponding g_{k}.

Following work by Graham and Diaconis I examine connectivity properties of these graphs when G is abelian and when G is a small symmetric group. (For instance, |V (Γ_{3}(Σ_{4}))| = 10,080!!). Pictures will be provided free of charge.

I will relate the size and connectivity properties of these graphs to classic counting problems of Phillip Hall.

seminars/comb/abstract.201110bid.txt · Last modified: 2020/01/29 14:03 (external edit)

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