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CORR
2011
Springer
2011
Springer
A Doubly Exponentially Crumbled Cake
Weconsiderthefollowingcakecuttinggame:AlicechoosesasetPofnpointsin thesquare(cake)[0,1]2,where(0,0)∈P;Bobcutsoutnaxis-parallelrectangles withdisjointinteriors,eachofthemhavingapointofPasthelowerleftcorner; Alicekeepstherest. IthasbeenconjecturedthatBobcanalwayssecureatleasthalfofthecake. Thisremainsunsettled,anditisnotevenknownwhetherBobcangetanypositive fractionindependentofn.WeprovethatifAlicecanforceBob’ssharetotend tozero,thenshemustuseverymanypoints;namely,topreventBobfromgaining morethan1/rofthecake,sheneedsatleast22Ω(r) points.
Real-time Traffic| Added | 13 May 2011 |
| Updated | 13 May 2011 |
| Type | Journal |
| Year | 2011 |
| Where | CORR |
| Authors | Tobias Christ, Andrea Francke, Heidi Gebauer, Jirí Matousek, Takeaki Uno |
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