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math.MG2013
Helly type theorems for the sum of vectors in a normed plane
Imre Bárány, Jesús Jerónimo-Castro
The main results here are two Helly type theorems for the sum of (at most) unit vectors in a normed plane. Also, we give a new characterization of centrally symmetric convex sets i…
math.MG2013
On a problem by Dol'nikov
Jesús Jerónimo-Castro, Alexander Magazinov, Pablo Soberón
In 2011 at an Oberwolfach workshop in Discrete Geometry, V. Dol'nikov posed the following problem. Consider three non-empty families of translates of a convex compact set in th…