4 problems

Fox–Grinshpun–Pach conjecture.

For $n>1$, let $Q_{n,n-1}(q)$ be the coefficient appearing in the conjectured Hilbert-series expansion of the Gallai algebra $\mathcal G_{n,k}$. Let $E(n-1,j)$ denote the second-or…

Linear-threshold conjecture. For any constant $c\geq 2$, there exists a $p_0$ such that for all integers $p\geq p_0$ and $k\geq p-c$,

For $n\geq GR_k(K_3)$, write … where $m$ and $r$ are nonnegative integers with $0\leq r\leq 5^{\lfloor(k-1)/2\rfloor}-1$. Let $g_k(K_3,n)$ denote the minimum number of monochromati…