A simple proof for open cups and caps

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00005045" target="_blank" >RIV/00216208:11320/07:00005045 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A simple proof for open cups and caps
Original language description
A set of points is a cup, if it lies on the graph of convex function. Similarly a set of points is a cap, if it lies on concave function. A cup/cap is open, if there is no point above the cup/cap. There is a Ramsey-type theorem, which says that if N is sufficiently large, we always find either open cup of size k or open cap of size l. We present a simple proof for open cups and open caps. Moreover we improve the bounds on N.
Czech name
Krátký důkaz pro otevřené šálky a čepice
Czech description
Mnozina bodu v rovine je salek, pokud lezi na grafu konvexni funkce. Podobne mnozina bodu je cepice, pokud lezi na grafu konkavni funkce. Mnozina je otevrene, pokud nad ni nelezi zadny dalsi bod. Ukazujeme jednoduchy dukaz vety, ze pro dostatecne velke N, kazda N-bodova mnozina v rovine obsahuje bud salek velikosti k a nebo cepici velikosti l.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
JC - Computer hardware and software
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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