Three-Monotone Interpolation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312956" target="_blank" >RIV/00216208:11320/15:10312956 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00454-015-9695-9" target="_blank" >http://dx.doi.org/10.1007/s00454-015-9695-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00454-015-9695-9" target="_blank" >10.1007/s00454-015-9695-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Three-Monotone Interpolation

Popis výsledku v původním jazyce

A function is called k-monotone if it is (k-2)-times differentiable and its (k-2)-nd derivative is convex. A planar point set is k-monotone interpolable if it lies on a graph of a k-monotone function. These notions have been studied in analysis, approximation theory, etc. since the 1940s. We show that 3-monotone interpolability is very nonlocal: we exhibit an arbitrarily large finite P for which every proper subset is 3-monotone interpolable but P itself is not. On the other hand, we prove a Ramsey-typeresult: for every n there exists N such that every N-point P with distinct x-coordinates contains an n-point Q such that Q or its vertical mirror reflection are 3-monotone interpolable. The analogs for k-monotone interpolability with k=1 and k=2 are classical theorems of Erdos and Szekeres, while the cases with k at least 4 remain open. We also investigate the computational complexity of deciding 3-monotone interpolability of a given point set. Using a known characterization, this decis

Název v anglickém jazyce

Three-Monotone Interpolation

Popis výsledku anglicky

A function is called k-monotone if it is (k-2)-times differentiable and its (k-2)-nd derivative is convex. A planar point set is k-monotone interpolable if it lies on a graph of a k-monotone function. These notions have been studied in analysis, approximation theory, etc. since the 1940s. We show that 3-monotone interpolability is very nonlocal: we exhibit an arbitrarily large finite P for which every proper subset is 3-monotone interpolable but P itself is not. On the other hand, we prove a Ramsey-typeresult: for every n there exists N such that every N-point P with distinct x-coordinates contains an n-point Q such that Q or its vertical mirror reflection are 3-monotone interpolable. The analogs for k-monotone interpolability with k=1 and k=2 are classical theorems of Erdos and Szekeres, while the cases with k at least 4 remain open. We also investigate the computational complexity of deciding 3-monotone interpolability of a given point set. Using a known characterization, this decis

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

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

54

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

3-21

Kód UT WoS článku

000355340300002

EID výsledku v databázi Scopus

2-s2.0-84930573405