4 problems

For a $1\times n$ strip of stamps, let $M(n)$ be the maximal number of ways to fold the strip over all mountain-valley assignments. Maximal-folding asymptotic conjecture. As…

Consider mountain-valley assignments for a $1\times n$ strip of stamps, and call an assignment maximally foldable when it has the greatest number of foldings among assignments for…

Let $S(m,k)$ denote the MV assignment with $m$ blocks, each of size $k$, and let $c(S(m,k))$ be its number of foldings. Equal-block asymptotic conjecture. For any fixed $m$ and suf…

Let an MV assignment be a sequence of mountain and valley blocks, and call it an equal-block mountain-valley assignment when all blocks have the same size. Let $c(A)$ denote the nu…