The very colorful Helly conjecture for d-Leray complexes and matroids
Let d\beq1d\beq 1d\beq1, r≥d+1r\geq d+1r≥d+1, 1≤m≤r1\leq m\leq r1≤m≤r and m≤k≤min{m+d,r}m\leq k\leq \min\{m+d,r\}m≤k≤min{m+d,r} be integers. Let VVV be a finite set with ∣V∣≥max{m+d,r}|V|\geq \max\{m+d,r\}∣V∣≥max{m+d,r}. Let XXX be a ddd-Leray simplicial com…