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UID:node-729@mathematics.ceu.edu
DTSTAMP:20180207T130000Z
DTSTART:20180207T130000Z
DTEND:20180207T130000Z
SUMMARY:Ramsey and Turán problem for sails
DESCRIPTION: Abstract: A triple system is linear if any two triples in it intersect in at most one point. There are 16 non-isomorphic linear triple systems, perhaphs the Pasch configuration is the most famous among them, obtained from the Fano plane by deleting one point and the three triples containing it. I introduce another member of the group, the sail: three triples through a point P and a fourth triple meeting the other three in points different from P. In an undergraduate research course during the summer of 2016 at BSM we tried to find which configurations C among the 16 have the Ramsey property: for sufficiently large admissible $n$ every 2-coloring of the triples of any Steiner triple system with n points, there is a monochromatic copy of C. We could decide this apart from one configuration: the sail. Then, in 2017 with Füredi we looked at the "Turán side of the coin", asking about the largest number of triples in a linear triple system on n points that does not contain sails. The answer is $n^2/9$ with... - http://mathematics.ceu.edu/events/2018-02-07/ramsey-and-turan-problem-sails
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