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arXiv · 1801.07238

On a Helly-type question for central symmetry

Alexey Garber·Edgardo Roldán-Pensado
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Abstract

We study a certain Helly-type question by Konrad Swanepoel. Assume that $X$ is a set of points such that every $k$-subset of $X$ is in centrally symmetric convex position, is it true that $X$ must also be in centrally symmetric convex position? It is easy to see that this is false if $k\le 5$, but it may be true for sufficiently large $k$. We investigate this question and give some partial results.

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Alexey Garber, Edgardo Roldán-Pensado. 2018-01-22. On a Helly-type question for central symmetry. https://doi.org/10.1007/s10998-018-0263-y

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