Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, June 09, 2011, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Zuzana Safernová (Charles Univ.)

On the nonexistence of k-reptile simplices in R^3 and R^4

A d-dimensional simplex S is called a k-reptile if it can be tiled without overlaps by simplices S_1,S_2,...,S_k that are all mutually congruent and similar to S. For d=2, k-reptile simplices (triangles) exist for many values of k and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, for d >= 3, only one construction of k-reptile simplices is known, the Hill simplices, and it provides only k of the form m^d, m=2,3,...

We prove that for d=3, k-reptile simplices (tetrahedra) exist only for k=m^3. This partially confirms a conjecture of Hertel, asserting that the only k-reptile tetrahedra are the Hill tetrahedra.

We also prove that for d=4, k-reptile simplices can exist only for k=m^2. For d=4 it remains to find out whether there really exist m^2-reptile simplices for m non-square and whether all m^4-reptile simplices are indeed Hill simplices.

First part is joint work with Jiri Matousek, the second one with Honza Kyncl.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login