Find the number of equivalency classes under a weird operation on permutations
Source: All-Russian MO 2023 Final stage 11.3
April 23, 2023
combinatorics
Problem Statement
In every row of a grid is written a permutation of the numbers . In one move you can choose a row and swap two non-adjacent numbers with difference . Find the largest possible , such that at any moment, no matter the operations made, no two rows may have the same permutations.