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SUMMARY:Ron Aharoni\, Colorful KKM and multiple cakes division
DESCRIPTION:In the “cake partition” problem n players have each a list of preferred parts for any partition of the [0\,1] interval (“cake”) into n sub-intervals. Woodall\, Stromquist and Gale proved independently that under mild conditions on the list of preferences (like continuity) there is always a partition and assignment of parts to the players\, in which every player gets a piece belonging to her list of preferred parts. In fact\, Gale proved a colorful version of the famous KKM theorem\, not realizing that this is the same problem\, but on the other hand\, proved the problem its proper setting. I will discuss the case of partitioning more than one cake – how many players can you make happy\, when there is a general number of cakes\, and general number of players. \nJoint work with Eli Berger\, Joseph Briggs\, Erel Segal-Halevi and Shira Zerbib.
URL:https://dimag.ibs.re.kr/event/2021-02-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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