2 problems

Rearrangement Conjecture. If $u$ and $v$ are Wilf equivalent, then they are rearrangements of each other; that is, they have the same multiset of letters. The converse is false: fo…

Let $w'$ be a word of length $k\ge 2$ whose letters are all distinct, and let $f(w',n,2)$ denote the maximum number of copies of $w'$ appearing in an $n\times n$ grid. Distinct-let…