Algebraic Combinatorics Seminar
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UNIVERSITY OF KENTUCKY **

ALGEBRAIC COMBINATORICS SEMINAR

845 PATTERSON OFFICE TOWER

FALL 2005

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"Empty convex hexagons"

Carlos Nicolas

University of Kentucky

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Monday, October 17, 2005

3:00 pm, 845 Patterson Office Tower

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Abstract:

Let P be a finite set of points in the plane, no three on a line. A
subset S of P is an empty convex set of P if the interior of conv(S)
contains no point of P. An empty convex 6-set of P is usually called
an empty convex hexagon. Using the Erdös-Szekeres theorem we show
that every set P with sufficiently many points contains an empty
convex hexagon, giving an affirmative answer to a question posed by
Erdös in 1977 that was open when I found my proof last semester.
(Apparently someone in Europe has independently found a proof while I
was typing my own.)