Monotonicity conjecture for balanced Radon partitions of Gaussian points
Let N,dfinNN,dfin\mathbb{N}N,dfinN satisfy N≥d+2N\geq d+2N≥d+2. For a partition [N]=A∪B[N]=A\cup B[N]=A∪B, let Pd(A,B)\mathbb{P}_d(A,B)Pd(A,B) denote the probability that (A,B)(A,B)(A,B) is a Radon partition among NNN independent ra…