Úkolem bude zkoumat dláždění vícerozměrných simplexů svými zmenšenými kopiemi (tzv. reptiles), a zjišťovat, pro které počty dlaždic taková dláždění existují.
The student will investigate tilings of higher-dimensional simplices by their shrinked copies (so-called reptiles), and determine for which numbers of tiles such tilings exist.
References
J. Matoušek, Nonexistence of 2-reptile simplices, Discrete and Computational Geometry: Japanese Conference, JCDCG 2004, vol. 3742 of Lecture Notes in Comput. Sci., Springer, Berlin (2005) 151-160; erratum at http://kam.mff.cuni.cz/~matousek/no2r-err.pdf.
J. Matoušek and Z. Safernová, On the nonexistence of k-reptile tetrahedra, Discrete Comput. Geom. 46(3) (2011), 599-609.
J. Kynčl and Z. Patáková, On the nonexistence of k-reptile simplices in R^3 and R^4, The Electronic Journal of Combinatorics 24 (2017), Issue 3, P3.1, 44 pp.
Preliminary scope of work
Více informací na https://kam.mff.cuni.cz/~kyncl/topics.
Preliminary scope of work in English
See https://kam.mff.cuni.cz/~kyncl/topics_eng for more information.
