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math.CO2017★ 3 cited
Bounding the size of an almost-equidistant set in Euclidean space
Andrey Kupavskii, Nabil H. Mustafa, Konrad J. Swanepoel
A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in $…
math.CO2017
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
Jesus A. De Loera, Xavier Goaoc, Frédéric Meunier +1
We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We…