Geodesic
Simplices and regular polygonal tori in Euclidean Ramsey theory
Miltiadis Karamanlis1
1National Technical University Of Athens
The electronic journal of combinatorics, Tome 29 (2022) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We show that any finite affinely independent set can be isometrically embedded into a regular polygonal torus, that is, the finite product of the vertex sets of some regular polygons. We apply this result in the context of Euclidean Ramsey Theory, highlighting the connection between the two most significant results in this field which were previously thought to be independent. In particular with a straightforward application of Kříž’s theorem we give an alternative proof of the fact that all finite affinely independent sets are Ramsey, a result which was originally proved by Frankl and Rödl.
DOI : 10.37236/10944
Classification : 05D10, 05C55
Mots-clés : finite affinely independent set, family of subsets, intersection pattern

Miltiadis Karamanlis  1

1 National Technical University Of Athens 
@article{10_37236_10944,
     author = {Miltiadis Karamanlis},
     title = {Simplices and regular polygonal tori in {Euclidean} {Ramsey} theory},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {3},
     doi = {10.37236/10944},
     zbl = {1498.05274},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10944/}
}
TY  - JOUR
AU  - Miltiadis Karamanlis
TI  - Simplices and regular polygonal tori in Euclidean Ramsey theory
JO  - The electronic journal of combinatorics
PY  - 2022
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/10944/
DO  - 10.37236/10944
ID  - 10_37236_10944
ER  - 
%0 Journal Article
%A Miltiadis Karamanlis
%T Simplices and regular polygonal tori in Euclidean Ramsey theory
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10944/
%R 10.37236/10944
%F 10_37236_10944
Miltiadis Karamanlis. Simplices and regular polygonal tori in Euclidean Ramsey theory. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/10944

Cité par Sources :