3 papers
math.CO2026
A Chain-Level Borsuk--Ulam Obstruction Proof of Norine's Antipodal-Coloring Conjecture
Hehui Wu, Ningyuan Yang
We prove Norine's conjecture: every red--blue edge-coloring of the \(n\)-dimensional hypercube \(Q_n\), \(n\geq2\), in which antipodal edges have opposite colors contains a monochr…
math.CO2025
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
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…