Geodesic
Generalized Schur numbers for \(x_1+ x_2+ c= 3x_3\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Let $r(c)$ be the least positive integer $n$ such that every two coloring of the integers $1,\ldots,n$ contains a monochromatic solution to $x_1 + x_2 + c = 3x_3$. Verifying a conjecture of Martinelli and Schaal, we prove that $$ r(c) = \left\lceil{2\lceil{2+c\over3}\rceil + c\over3}\right\rceil, $$ for all $c \ge 13$, and $$ r(c) = \left\lceil{3\lceil{3-c\over2}\rceil - c\over2}\right\rceil, $$ for all $c \le -4$.
DOI : 10.37236/194
Classification : 05D10 
@article{10_37236_194,
     author = {Andr\'e E. K\'ezdy and Hunter S. Snevily and Susan C. White},
     title = {Generalized {Schur} numbers for \(x_1+ x_2+ c= 3x_3\)},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/194},
     zbl = {1186.05117},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/194/}
}
TY  - JOUR
AU  - André E. Kézdy
AU  - Hunter S. Snevily
AU  - Susan C. White
TI  - Generalized Schur numbers for \(x_1+ x_2+ c= 3x_3\)
JO  - The electronic journal of combinatorics
PY  - 2009
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/194/
DO  - 10.37236/194
ID  - 10_37236_194
ER  - 
%0 Journal Article
%A André E. Kézdy
%A Hunter S. Snevily
%A Susan C. White
%T Generalized Schur numbers for \(x_1+ x_2+ c= 3x_3\)
%J The electronic journal of combinatorics
%D 2009
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/194/
%R 10.37236/194
%F 10_37236_194
André E. Kézdy; Hunter S. Snevily; Susan C. White. Generalized Schur numbers for \(x_1+ x_2+ c= 3x_3\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/194

Cité par Sources :