subsimplices

— The conjecture asserts that for each integers r,dgt;0 and each continuous map f#92;colon#92;Delta#92;to#92;mathbbRᵈ of the (d#43;1)(r-1)-dimensional simplex #92;Delta there are pairwise disjoint subsimplices #92;sigma#95;1,#92;ldots,#92;sigma#95;r#92;subset#92;Delta such that f(#92;sigma#95;1)#92;cap#92;ldots#92;capf(#92;sigma#95;r)#92;ne#92;emptyset. A counterexample was found in a series of papers by M. \"Ozaydin, M.