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Number of natural-valued non-contracted Lipschitz functions

Source: Romanian National Olympiad 2014, Grade X, Problem 3

March 2, 2019
functionalgebra

Problem Statement

Let n n be a natural number, and A A the set of the first n n natural numbers. Find the number of nondecreasing functions f:A⟶A f:A\longrightarrow A that have the property x,y∈A  ⟹  ∣f(x)−f(y)∣≤∣x−y∣. x,y\in A\implies |f(x)-f(y)|\le |x-y|.
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