Multiplicity of monochromatic solutions to x+y < z

作者：Kosek Wojciech^*; Robertson Aaron; Sabo Dusty; Schaal Daniel

来源：Journal of Combinatorial Theory - Series A, 2010, 117(8): 1127-1135.

DOI：10.1016/j.jcta.2010.04.004

• Schur numbers
• Asymptotics
• Ramsey theory

For integers n >= 1 and k >= 0, let M(k)(n) represent the minimum number of monochromatic solutions to x + y < z over all 2-colorings of {k + 1, k + 2, ... , k + n}. We show that for any k >= 0, M(k)(n) = Cn(3) (1 o(k)(1)), where C = 1/12(1+2 root 2)(2) approximate to 0.005686. A structural result is also proven, which can be used to determine the exact value of M(k)(n) for given k and n.

• 出版日期2010-11