Structural properties of extremal asymmetric colorings
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Structural properties of extremal asymmetric colorings
|
|
| Creator |
Verbitsky, O.
|
|
| Description |
Let Ω be a space with probability measure µ for which the notion of symmetry is defined. Given A ⊆ Ω, let ms(A) denote the supremum of µ(B) over symmetric B ⊆ A. An r-coloring of Ω is a measurable map χ : Ω → {1, . . . , r} possibly undefined on a set of measure 0. Given an r-coloring χ, let ms(Ω; χ) = max₁≤i≤r ms(χ⁻¹ (i)). With each space Ω we associate a Ramsey type number ms(Ω, r) = infχ ms(Ω; χ). We call a coloring χ congruent if the monochromatic classes χ⁻¹ (1), . . . , χ⁻¹ (r) are pairwise congruent, i.e., can be mapped onto each other by a symmetry of Ω. We define ms* (Ω, r) to be the infimum of ms(Ω; χ) over congruent χ. We prove that ms(S¹ , r) = ms* ([0, 1), r) for the unitary interval of reals considered with central symmetry, and explore some other regularity properties of extremal colorings for various spaces.
|
|
| Date |
2019-06-17T10:52:28Z
2019-06-17T10:52:28Z 2003 |
|
| Type |
Article
|
|
| Identifier |
Structural properties of extremal asymmetric colorings / O. Verbitsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 92–117. — Бібліогр.: 12 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 05D10. http://dspace.nbuv.gov.ua/handle/123456789/155696 |
|
| Language |
en
|
|
| Relation |
Algebra and Discrete Mathematics
|
|
| Publisher |
Інститут прикладної математики і механіки НАН України
|
|