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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

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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Počet stran výsledku

6

Strana od-do

191-196

Název nakladatele

Scuola Normale Superiore

Místo vydání

Pisa, Italy

Místo konání akce

Pisa, Italy

Datum konání akce

9. 9. 2013

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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