3 problems

The algebraicity–diagonal–global-boundedness conjecture. The following statements are equivalent:

Christol's conjecture. Every D-finite globally bounded function is the diagonal of a rational function.

Let $S_k$ be the symmetric group on $k$ letters. For a fixed finite set of patterns $\subset S_k$, let $C_n(\mathcal{F})$ be the number of permutations in $S_n$ avoiding every patt…