Covering radii are not matroid invariants
We show by example that the covering radius of a binary linear code is not generally determined by the Tutte polynomial of the matroid. This answers Problem 361 (P.J. Cameron (Ed.), Research problems, Discrete Math. 231 (2001) 469-478). e Tutte polynomial of the matroid. This answers Problem 361 (P.J. Cameron (Ed.), Research problems, Discrete Math. 231 (2001) 469-478).
The spaces of configurations of non-$k$-overlapping discs have been studied as a bimodule over the little discs operad. In fact, the spaces form a filtered operad. We define and study the induced structure on the homology.