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LOWER BOUNDS ON GEOMETRIC RAMSEY FUNCTIONS

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286487" target="_blank" >RIV/00216208:11320/14:10286487 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1137/140963716" target="_blank" >http://dx.doi.org/10.1137/140963716</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/140963716" target="_blank" >10.1137/140963716</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    LOWER BOUNDS ON GEOMETRIC RAMSEY FUNCTIONS

  • Original language description

    We continue a sequence of recent works studying Ramsey functions for semialgebraic predicates in R-d. A k-ary semialgebraic predicate Phi(x(1), ..., x(k)) on R-d is a Boolean combination of polynomial equations and inequalities in the kd coordinates of kpoints x(1), ..., x(k) is an element of R-d. A sequence P = (p(1), ..., p(n)) of points in R-d is called Phi-homogeneous if either Phi(p(i1), ..., p(ik)) holds for all choices 1 {= i(1) < ... < i(k) {= n, or it holds for no such choice. The Ramsey function R-Phi(n) is the smallest N such that every point sequence of length N contains a Phi-homogeneous subsequence of length n. Conlon et al. [Trans. Amer. Math. Soc., 366 (2013), pp. 5043-5065] constructed the first examples of semialgebraic predicates with the Ramsey function bounded from below by a tower function of arbitrary height: for every k }= 4, they exhibit a k-ary Phi in dimension 2(k-4) with R-Phi bounded below by a tower of height k - 1. We reduce the dimension in their constr

  • 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

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

    S - Specificky vyzkum na vysokych skolach

Others

  • Publication year

    2014

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    SIAM Journal on Discrete Mathematics

  • ISSN

    0895-4801

  • e-ISSN

  • Volume of the periodical

    28

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    11

  • Pages from-to

    1960-1970

  • UT code for WoS article

    000346844200020

  • EID of the result in the Scopus database