MathDB
Changing permutations to get the position

Source: Belarus TST 2024

July 17, 2024
permutationscombinatorics

Problem Statement

Two permutations of 1,,n1,\ldots, n are written on the board: a1,,ana_1,\ldots,a_n b1,,bnb_1,\ldots,b_n A move consists of one of the following two operations: 1) Change the first row to ba1,,banb_{a_1},\ldots,b_{a_n} 2) Change the second row to ab1,,abna_{b_1},\ldots,a_{b_n} The starting position is: 2134n2134\ldots n 234n1234\ldots n1 Is it possible by finitely many moves to get: 2314n2314\ldots n 234n1234 \ldots n1? D. Zmiaikou