MathDB

Consider the set

S

of permutations of

1, 2, \dots, 2022

such that for all numbers

k

in the permutation, the number of numbers less than

k

that follow

k

is even.
For example, for

n=4; S = \{[3,4,1,2]; [3,1,2,4]; [1,2,3,4]; [1,4,2,3]\}

|S| = (a!)^b

where

a, b \in \mathbb{N}

, then find the product

ab

Problem Statement