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 is a classic problem related to **Erdős-Szekeres theory** on the existence of increasing and decreasing subsequences within sequences of integers. The goal is to construct a permutation of the integers from \( 

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.

This problem involves creating a permutation of integers from 1 to mn with no increasing subsequence of length m + 1 and no decreasing subsequence of length n + 1, using principles from Erdős-Szekeres Theorem. Suitable for advanced high school and undergraduate students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation