Higher-order Erdos-Szekeres theorems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10125726" target="_blank" >RIV/00216208:11320/12:10125726 - isvavai.cz</a>
Result on the web
<a href="http://dl.acm.org/ft_gateway.cfm?id=2261264&ftid=1240072&dwn=1&CFID=261492957&CFTOKEN=16910344" target="_blank" >http://dl.acm.org/ft_gateway.cfm?id=2261264&ftid=1240072&dwn=1&CFID=261492957&CFTOKEN=16910344</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1145/2261250.2261264" target="_blank" >10.1145/2261250.2261264</a>
Alternative languages
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 $sqrt N$ points. Another, equally famous theoremfrom 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 bothof these theorems members of an infinite family of Ramsey-type results. First we define a (k+1)-tuple $Ksubseteq P$ 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 $Ssubseteq P$ is kth-order monotone if its (k+1)-tuples are all positive or all negative. We investigate quantitative bound for the corresponding Ramsey-type result (i.e., how large kth-order monotone subsequence
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
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)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the 28th Annual ACM Symposium on Computational Geometry
ISBN
978-1-4503-1299-8
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
81-90
Publisher name
Association for Computing Machinery
Place of publication
New York, USA
Event location
Chapel Hill
Event date
Jun 17, 2012
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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