On the nonexistence of k-reptile simplices in R^3 and R^4
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190773" target="_blank" >RIV/00216208:11320/13:10190773 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007/978-88-7642-475-5_31" target="_blank" >http://link.springer.com/chapter/10.1007/978-88-7642-475-5_31</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-88-7642-475-5_31" target="_blank" >10.1007/978-88-7642-475-5_31</a>
Alternative languages
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 without overlaps by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d=2, triangular k-reptiles exist for many values ofk 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 Matousek and the second author that for d=3, k-reptile tetrahedra can exist only for k=m^3. We also 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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
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
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
The Seventh European Conference on Combinatorics, Graph Theory and Applications
ISBN
978-88-7642-474-8
ISSN
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e-ISSN
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Number of pages
6
Pages from-to
191-196
Publisher name
Scuola Normale Superiore
Place of publication
Pisa, Italy
Event location
Pisa, Italy
Event date
Sep 9, 2013
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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