What is an ordered array?
Borrowing the definition from Gaurang Tandon's question:

An array $A[1...n]$ is said to be k-ordered if
$$A[i - k] \leq A[i] \leq A[i + k]$$
for all $i$ such that $k &lt; i \leq n - k$.
For example, the array $A = [1, 4, 2, 6, 3, 7, 5, 8]$ is 2 ordered.

I must also say that I've never seen a similar definition before (and I find it to be quite un-useful, but maybe it is important somewhere).
Another definition I have seen, extends the ordering to $k$-dimensional objects. For instance, with two dimensions:

Given vectors $v=(v_1,v_2)$ and $u=(u_1,u_2)$,  we say that $v&gt;u$ in a 2-ordering if
$$v_1 &gt; u_1$$
or if
$$ v_1=u_1 \text{ and } v_2&gt;u_2$$

Then, an array of vectors $v[1...n]$ is $2$-ordered if for every $i$, $v[i]&lt;v[i+1]$ via the above 2-ordering.