LOWER BOUNDS ON GEOMETRIC RAMSEY FUNCTIONS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286870" target="_blank" >RIV/00216208:11320/14:10286870 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1145/2582112.2582146" target="_blank" >http://dx.doi.org/10.1145/2582112.2582146</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/2582112.2582146" target="_blank" >10.1145/2582112.2582146</a>

Jazyk výsledku

angličtina

Název v původním jazyce

LOWER BOUNDS ON GEOMETRIC RAMSEY FUNCTIONS

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

LOWER BOUNDS ON GEOMETRIC RAMSEY FUNCTIONS

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the thirtieth annual symposium on Computational geometry

ISBN

978-1-4503-2594-3

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

558-564

Název nakladatele

ACM

Místo vydání

New York

Místo konání akce

Kyoto

Datum konání akce

8. 6. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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