Fast algorithms, rigorous proofs.

Dhruv Ajmera

arXiv

A superpermutation is a sequence that contains every permutation of n distinct symbols as a contiguous substring. For instance, a valid example for three sym bols is a sequence that contains all six permutations. This paper introduces a new algorithm that constructs such sequences more efficiently than existing recursive and graph-theoretic methods. Unlike traditional techniques that suffer from scalability and factorial memory demands, the proposed approach builds super permutations directly and compactly. This improves memory usage, enabling the construction of larger sequences previously considered impractical.