Three-Monotone Interpolation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Three-Monotone Interpolation
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Computational Geometry
ISSN
0179-5376
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
3-21
UT code for WoS article
000355340300002
EID of the result in the Scopus database
2-s2.0-84930573405