BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christoph Spiegel (Zuse Institute Berlin) DTSTART:20250521T150000Z DTEND:20250521T152500Z DTSTAMP:20260423T041621Z UID:CANT2025/29 DESCRIPTION:Title: An unsure talk on an un-Schur problem\nby Christoph Spiegel (Zuse In stitute Berlin) as part of Combinatorial and additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor) .\n\nAbstract\nGraham\, R\\" odl\, and Ruci\\' nski originally posed the p roblem of determining the minimum number of monochromatic Schur triples th at must appear in any 2-coloring of the first $n$ integers. This question was subsequently resolved independently by Datskovsky\, Schoen\, and Rober tson and Zeilberger. Here we suggest studying a natural anti-Ramsey varian t of this question and establish the first non-trivial bounds by proving t hat the maximum fraction of Schur triples that can be rainbow in a given 3 -coloring of the first n integers is at least 0.4 and at most 0.66656. We conjecture the lower bound to be tight. This question is also motivated by a famous analogous problem in graph theory due to Erd\\H os and S\\' os r egarding the maximum number of rainbow triangles in any 3-coloring of $K_n $\, which was settled by Balogh\, et al. \nThis is joint work with Olaf Pa rczyk.\n LOCATION:https://researchseminars.org/talk/CANT2025/29/ END:VEVENT END:VCALENDAR