Multiset permutation generation by transpositions

TL;DR

This paper introduces a novel algorithm for generating all multiset permutations using transpositions, emphasizing adjacent swaps and a specific transposition condition to efficiently produce permutations with minimal storage.

Contribution

The paper presents a new permutation generation algorithm for multisets based solely on transpositions, with a unique condition for non-adjacent swaps to improve efficiency.

Findings

Efficient permutation generation with minimal storage

Uses only transpositions, favoring adjacent swaps

Imposes a specific condition for non-adjacent transpositions

Abstract

This paper proposes a new algorithm for generating all permutations of multisets. The method uses transpositions only and adjacent transpositions are favoured. The algorithm requires a strong homogeneous transposition condition: non-adjacent transpositions are allowed only if all elements between the two permuted elements are equal to the smallest of those two elements. The storage required by the algorithm is small.