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
—