Harmonic LCM patterns and sunflower-free capacity

Quanyu Tang, Shengtong Zhang

Fix an integer $k\ge 3$. Call a set $A\subseteq [N]$ LCM-$k$-free if it does not contain distinct $a_1,\dots ,a_k$ such that $\mathrm{lcm}(a_i,a_j)$ is the same for all $1\le i<j\le…