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David Biddle (Binghamton)

On the Size and Connectivity of Graphs of Generating Sets of Finitely Generated Groups

Abstract for the Combinatorics and Algebra Seminars 2011 October 25

Let G be a finitely generated group with minimal generating set of size d. For each t ≥ d let Γt = Γt(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 gi multiplied on left or right by gj±1, and all other g'k are the same as the corresponding gk.

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 (Γ34))| = 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.

1) g1, …, gt), (g'1, …, g't
seminars/comb/abstract.201110bid.txt · Last modified: 2020/01/29 14:03 (external edit)