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%2F17%3A10360665" target="_blank" >RIV/00216208:11320/17:10360665 - isvavai.cz</a>

Výsledek na webu

<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

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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 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&gt;=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.

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 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&gt;=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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

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Svazek periodika

24

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

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Kód UT WoS článku

000414863600008

EID výsledku v databázi Scopus

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