Unranking permutations in transposition order and linear time

TL;DR

This paper introduces a linear-time algorithm for unranking permutations in transposition order, enabling efficient generation of permutations that differ by a single transposition.

Contribution

The paper presents the first linear-time algorithm for unranking permutations in transposition order, improving efficiency over previous methods.

Findings

Algorithm operates in linear time

Permutations differ by a single transposition

Efficient permutation generation for large sets

Abstract

An algorithm is presented for unranking permutations in transposition order: Given a seed s\in N, the algorithm produces a permutation P(s) that differs from the permutation P(s+1) by the transposition of two elements.