Name
Abstract | ||
|---|---|---|
Given a space endowed with symmetry, we dene ms(;r )t o be the maximum of m such that for any r-coloring of there exists a monochromatic symmetric set of size at least m. We consider a wide range of spaces including the discrete and continuous segmentsf1;:::;ng and (0; 1) with central symmetry, geometric gures with the usual symmetries of Euclidean space, and Abelian groups with a natural notion of central symmetry. We observe that ms(f1;:::;ng;r )a ndms((0; 1);r) are closely related, prove lower and upper bounds for ms((0; 1); 2), and nd asymptotics of ms((0; 1);r )f orr increasing. The exact value of ms(;r) is determined for gures of revolution, regular polygons, and multi-dimensional parallelopipeds. We also discuss problems of a slightly dierent flavor and, in particular, prove that the minimal r such that there exists an r-coloring of the k-dimensional integer grid without innite monochromatic symmetric subsets is k +1 . |
Year | Venue | Keywords |
|---|---|---|
2000 | Electr. J. Comb. | abelian group,euclidean space |
Field | DocType | Volume |
Integer,Discrete mathematics,Abelian group,Combinatorics,Symmetric set,Regular polygon,Euclidean space,Omega,Asymptotic analysis,Homogeneous space,Mathematics | Journal | 7 |
Citations | PageRank | References |
5 | 1.66 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| O. V. Verbitsky | 2 | 5 | 2.00 |
| Ya. Vorobets | 3 | 5 | 1.66 |