On a Rado type problem for homogeneous second order linear recurrences
The electronic journal of combinatorics, Tome 17 (2010)
In this paper we introduce a Ramsey type function $S(r;a,b,c)$ as the maximum $s$ such that for any $r$-coloring of ${\Bbb N}$ there is a monochromatic sequence $x_1,x_2,\ldots,x_s$ satisfying a homogeneous second order linear recurrence $ax_i+bx_{i+1}+cx_{i+2}=0$, $1\leq i\leq s-2$. We investigate $S(2;a,b,c)$ and evaluate its values for a wide class of triples $(a,b,c)$.
@article{10_37236_310,
author = {Hayri Ardal and Zden\v{e}k Dvo\v{r}\'ak and Veselin Jungi\'c and Tom\'a\v{s} Kaiser},
title = {On a {Rado} type problem for homogeneous second order linear recurrences},
journal = {The electronic journal of combinatorics},
year = {2010},
volume = {17},
doi = {10.37236/310},
zbl = {1215.05196},
url = {http://geodesic.mathdoc.fr/articles/10.37236/310/}
}
TY - JOUR AU - Hayri Ardal AU - Zdeněk Dvořák AU - Veselin Jungić AU - Tomáš Kaiser TI - On a Rado type problem for homogeneous second order linear recurrences JO - The electronic journal of combinatorics PY - 2010 VL - 17 UR - http://geodesic.mathdoc.fr/articles/10.37236/310/ DO - 10.37236/310 ID - 10_37236_310 ER -
%0 Journal Article %A Hayri Ardal %A Zdeněk Dvořák %A Veselin Jungić %A Tomáš Kaiser %T On a Rado type problem for homogeneous second order linear recurrences %J The electronic journal of combinatorics %D 2010 %V 17 %U http://geodesic.mathdoc.fr/articles/10.37236/310/ %R 10.37236/310 %F 10_37236_310
Hayri Ardal; Zdeněk Dvořák; Veselin Jungić; Tomáš Kaiser. On a Rado type problem for homogeneous second order linear recurrences. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/310
Cité par Sources :