Higher-order Erdos-Szekeres theorems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10145705" target="_blank" >RIV/00216208:11320/13:10145705 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2013.04.020" target="_blank" >http://dx.doi.org/10.1016/j.aim.2013.04.020</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2013.04.020" target="_blank" >10.1016/j.aim.2013.04.020</a>

Result language
angličtina
Original language name
Higher-order Erdos-Szekeres theorems
Original language description
Let P = (p(1), p(2),...,p(N)) be a sequence of points in the plane, where p(i) = (x(i), y(i)) and x(1) < x(2) < ... < x(N). A famous 1935 Erdos-Szekeres theorem asserts that every such P contains a monotone subsequence S of inverted right perpendicular root N inverted left perpendicular points. Another, equally famous theorem from the same paper implies that every such P contains a convex or concave subsequence of Omega(log N) points. Monotonicity is a property determined by pairs of points, and convexity concerns triples of points. We propose a generalization making both of these theorems members of an infinite family of Ramsey-type results. First we define a (k + 1)-tuple K subset of P to be positive if it lies on the graph of a function whose kth derivative is everywhere nonnegative, and similarly for a negative (k + 1)-tuple. Then we say that S subset of P is kth-order monotone if its (k + 1)-tuples are all positive or all negative. We investigate a quantitative bound for the corre
Czech name
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Czech description
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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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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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