Digital Repository of Luhansk Taras Shevchenko National University
Structural properties of extremal asymmetric colorings
JavaScript is disabled for your browser. Some features of this site may not work without it.
| dc.contributor.author | Verbitsky, Oleg | |
| dc.date.accessioned | 2015-10-21T10:49:30Z | |
| dc.date.available | 2015-10-21T10:49:30Z | |
| dc.date.issued | 2003 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/81 | |
| dc.description | Let be a space with probability measure μ for which the notion of symmetry is defined. Given A µ , let ms(A) denote the supremum of μ(B) over symmetric B µ A. An r-coloring of is a measurable map  : ! {1, . . . , r} possi- bly undefined on a set of measure 0. Given an r-coloring Â, let ms(; Â) = max1·i·r ms(Â−1(i)). With each space we associate a Ramsey type number ms(, r) = infÂms(; Â). We call a col- oring  congruent if the monochromatic classes Â−1(1), . . . , Â−1(r) are pairwise congruent, i.e., can be mapped onto each other by a symmetry of . We define ms?(, r) to be the infimum of ms(; Â) over congruent Â. We prove that ms(S1, r) = ms?(S1, r) for the unitary circle S1 endowed with standard symmetries of a plane, estimate 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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Луганский национальный университет им. Т. Шевченко | uk_UA |
| dc.title | Structural properties of extremal asymmetric colorings | uk_UA |
| dc.type | Article | uk_UA |
Files in this item
This item appears in the following Collection(s)
-
Статті
This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian and Russian mathematician, one of the founder of our journal Professor Rostislav Grigorchuk, who was 50 years of age on February 23, 2003.