Erdős–Purdy–Agarwal–Sharir conjecture on congruent simplices
Let d≥4d\geq 4d≥4, let k≤dk\leq dk≤d, and let C(d,k,n)\mathrm{C}(d,k,n)C(d,k,n) denote the maximum, over all kkk-vertex simplices SSS and all nnn-element sets P⊆RdP\subseteq\mathbb{R}^dP⊆Rd, of the number of…