So that the resulting sequence has no increasing subsequence of length $\ge r$ and no decreasing subsequence of length $\ge s$.
2026-04-22 16:21:10.1776874870
For any $r, s \in \mathbb{N}$, show how to order the numbers $1, 2, \ldots , rs$
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$$s,s-1,s-2,\ldots,1,\quad 2s,2s-1,\ldots, s+1,\quad 3s,3s-1,\ldots $$ A decreasing sequence must stay within a block, an increasing sequence cannot have more than one term from the same block.