MathDB

|f(z) - z| <= k, for every k, each k-jumpy map is composition of 1-jumpy maps?

Source: Balkan MO Shortlist 2013 A7 BMO

March 9, 2020

compositionalgebramappingbijectionbijective functionpositive integers

Problem Statement

Suppose that

k

is a positive integer. A bijective map

f : Z \to 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.