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* Princeton Discrete Math Seminar *
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Speaker: Carla Groenland (U Oxford)
Thursday 21st November, 3:00 in Fine Hall 224.
Title: Cyclically covering subspaces
A subspace of F_2^n is called "cyclically covering" if every vector in F_2^n
has a cyclic shift which is inside the subspace. Let h_2(n) denote the largest
possible codimension of a cyclically covering subspace of F_2^n. We show that
h_2(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.
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Next week: No talk. Week after, TBA
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