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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10360665" target="_blank" >RIV/00216208:11320/17:10360665 - isvavai.cz</a>
Result on the web
<a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p1" target="_blank" >http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p1</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
On the nonexistence of k-reptile simplices in R^3 and R^4
Original language description
A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d=2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2 + b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d>=3, have k=m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d=3, k-reptile tetrahedra can exist only for k=m^3. We then prove a weaker analogue of this result for d=4 by showing that four-dimensional k-reptile simplices can exist only for k=m^2.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)