Rule based lexicographical permutation sequences

TL;DR

This paper introduces a rule-based method for generating permutation sequences efficiently, leveraging regularity in transition rules to optimize time and space complexity.

Contribution

It presents a novel rule-based approach that enables permutation sequences to be produced in optimized time and space, improving over previous methods.

Findings

Sequence generation in O(3n!) time

Uses O(n^3) space for storage

Exploits regularity in transition rules

Abstract

In a permutation sequence built by means of sub permutations the transition between successive permutations are subject to a set of n(n - 1)/2 rules that group into n - 1 matrices with a high degree of regularity. By means of these rules the sequence can be produced in O(3n!) time and O(n^3) space.