On Schur's conjecture

Abstract

Let P be a set of n points in Rd. It was conjectured by Schur that the maximum number of (d−1)-dimensional regular simplices of edge length diam(P ), whose every vertex belongs to P , is n. We prove this statement under the condition that any two of the simplices share at least d − 2 vertices. It is left as an open question to decide whether this condition… (More)
DOI: 10.1016/j.endm.2013.10.033

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