Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Friday, June 18, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Jiří Matoušek (Charles Univ.)

Simplex Reptiles Could Help the Net Police, But Probably They Do Not Exist

A polyhedron P in R^d is called a k-reptile if P can be tiled without overlaps by k similar copies of itself that are all congruent (k>1). For example, the right isoceles triangle in the plane is a 2-reptile. I will (try to) prove that for d>2 there are no d-dimensional simplices that are 2-reptiles. It seems plausible, but maybe hard to prove, that if a d-simplex is a k-reptile, d>2, then k must be at least 2^d. This (very incomplete) investigation has been motivated by probabilistic encoding of the routes of messages on the Internet.

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