Geodesic
A note on a Ramsey-type problem for sequences
Andrzej Dudek1
1Western Michigan University
The electronic journal of combinatorics, Tome 21 (2014) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

Two sequences $\{x_i\}_{i=1}^{t}$ and $\{y_i\}_{i=1}^t$ of distinct integers are similar if their entries are order-isomorphic. Let $f(r,X)$ be the length of the shortest sequence $Y$ such that any $r$-coloring of the entries of $Y$ yields a monochromatic subsequence that is also similar to $X$. In this note we show that for any fixed non-monotone sequence $X$, $f(r,X)=\Theta(r^2)$, otherwise, for a monotone $X$, $f(r,X)=\Theta(r)$.
DOI : 10.37236/4217
Classification : 05A05, 05D10
Mots-clés : sequences, permutations, Ramsey problems

Andrzej Dudek  1

1 Western Michigan University 
@article{10_37236_4217,
     author = {Andrzej Dudek},
     title = {A note on a {Ramsey-type} problem for sequences},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {3},
     doi = {10.37236/4217},
     zbl = {1301.05009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4217/}
}
TY  - JOUR
AU  - Andrzej Dudek
TI  - A note on a Ramsey-type problem for sequences
JO  - The electronic journal of combinatorics
PY  - 2014
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/4217/
DO  - 10.37236/4217
ID  - 10_37236_4217
ER  - 
%0 Journal Article
%A Andrzej Dudek
%T A note on a Ramsey-type problem for sequences
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/4217/
%R 10.37236/4217
%F 10_37236_4217
Andrzej Dudek. A note on a Ramsey-type problem for sequences. The electronic journal of combinatorics, Tome 21 (2014) no. 3. doi: 10.37236/4217

Cité par Sources :