A Geometric Proof of the Colored Tverberg Theorem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125606" target="_blank" >RIV/00216208:11320/12:10125606 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00454-011-9368-2" target="_blank" >http://dx.doi.org/10.1007/s00454-011-9368-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00454-011-9368-2" target="_blank" >10.1007/s00454-011-9368-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Geometric Proof of the Colored Tverberg Theorem

Popis výsledku v původním jazyce

The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in R^(d) of cardinality (d+1)t, partitioned into t-point subsets C_1,C_2,...,C_(d+1) (which we think of as color classes; e.g., the points of C_1are red, the points of C_2 blue, etc.), there exist r disjoint sets R_1, R_2, ... ,R_r subset of C that are rainbow, meaning that the size of the intersection of R_i and C_j is at most 1 for every i, j, and whose convex hulls all have a common point. Allknown proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojevic, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof moreconcrete and intuitive, and accessible to a wider audience.

Název v anglickém jazyce

A Geometric Proof of the Colored Tverberg Theorem

Popis výsledku anglicky

The colored Tverberg theorem asserts that for every d and r there exists t=t(d,r) such that for every set C in R^(d) of cardinality (d+1)t, partitioned into t-point subsets C_1,C_2,...,C_(d+1) (which we think of as color classes; e.g., the points of C_1are red, the points of C_2 blue, etc.), there exist r disjoint sets R_1, R_2, ... ,R_r subset of C that are rainbow, meaning that the size of the intersection of R_i and C_j is at most 1 for every i, j, and whose convex hulls all have a common point. Allknown proofs of this theorem are topological. We present a geometric version of a recent beautiful proof by Blagojevic, Matschke, and Ziegler, avoiding a direct use of topological methods. The purpose of this de-topologization is to make the proof moreconcrete and intuitive, and accessible to a wider audience.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/1M0545" target="_blank" >1M0545: Institut Teoretické Informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Discrete and Computational Geometry

ISSN

0179-5376

e-ISSN

—

Svazek periodika

47

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

245-265

Kód UT WoS článku

000299057200002

EID výsledku v databázi Scopus

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