I want to find an example of a sequence of n=rs distinct numbers where there is not an increasing sequence of length s or a decreasing sequence of length r, hence showing that the bound given by Erdős-Szekeres is the best possible.
However, having tried several options, I cannot come up with a single example. I thought of using r=1=s, but this gives a single element sequence which is both increasing and decreasing so does not work.
I am starting to think it cannot be possible. Is there such an example?