Question 44
Suppose that $k$ is a positive integer. A bijective map $f: \mathbb{Z} \to \mathbb{Z}$ is said to be $k$-jumpy if $|f(z) - z| \le k$ for all integers $z$.
Is it that case that for every $k$, each $k$-jumpy map is a composition of 1-jumpy maps?
*It is well known that this is the case when the support of the map is finite.*
Is it that case that for every $k$, each $k$-jumpy map is a composition of 1-jumpy maps?
*It is well known that this is the case when the support of the map is finite.*