Monochromatic progressions in random colorings |
| |
Authors: | Sujith Vijay |
| |
Institution: | School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram-695016, Kerala, India |
| |
Abstract: | Let and where and arbitrarily slowly as . We show that the probability of a random 2-coloring of containing a monochromatic k-term arithmetic progression approaches 1, and the probability of a random 2-coloring of containing a monochromatic k-term arithmetic progression approaches 0, as . This improves an upper bound due to Brown, who had established an analogous result for . |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|