2 problems

For $n\ge 2$, let $S(n)$ be the $n$th Schur number. Let $L(n)$ be the least length such that every sequence $A$ in $\mathbb N_+$ with $|A|=L(n)$ and average $\mu(A)\le n$ satisfies…

For $n\ge 2$, let $S(n)$ denote the $n$th Schur number. The recursive Schur-number upper-bound conjecture. … This conjecture follows from the preceding conjecture on $L(n)$ togethe…