3 papers
math.CO2024
Element-Distinct Solution For Rado's Theorem
Ningyuan Yang, Tianyi Tao
In this paper, we present a simplified proof of Rado's Theorem and demonstrate that when an integer matrix satisfies the column condition and has an elem…
math.CO2024
Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers
Wen Huang, Song Shao, Tianyi Tao +2
In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lam…
math.CO2024
Finding Product and Sum Patterns in non-commutative settings
T. Y. Tao, Neil N. Y. Yang
Hindman conjectured that any finite partition of has a monochromatic . Recently, Bowen proved the result for all 2-partition. In this paper, we extend…