A subspace of 𝔽2n is called cyclically covering if every vector in 𝔽2n has a cyclic shift which is inside the subspace. Let h2(n) denote the largest possible codimension of a cyclically covering subspace of 𝔽2n. We show that h2(p) = 2 for every prime p such that 2 is a primitive root modulo p, which, assuming Artin’s conjecture, answers a question of Peter Cameron from 1991. In this talk, I will try to explain how we reduce the problem to a problem on finding odd subgraphs in which each vertex has odd outdegree in directed Cayley graphs, how additive combinatorics comes to the rescue and which open problems I would like to see solved. This is joint work with James Aaronson and Tom Johnston.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
