Let m and n be positive integers. Exhibit an arrangement of the integersbetween 1 and mn which has no increasing subsequence of length m + 1,and no decreasing subsequence of length n + 1.

This problem is a well-known application of the **Erdős–Szekeres theorem**, which deals with sequences and their increasing and decreasing subsequences. In this case, we need to arrange the integers between 

Let m and n be positive integers. Exhibit an arrangement of the integers between 1 and mn which has no increasing subsequence of length m + 1, and no decreasing subsequence of length n + 1.

Learn how to arrange the integers between 1 and mn such that no increasing subsequence of length m + 1 or decreasing subsequence of length n + 1 exists. This solution uses the Erdős–Szekeres theorem, a well-known result in combinatorics. Suitable for advanced high school or undergraduate students.

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