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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

  • 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

  • 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