2025/04/29 by Dhruv Ajmera, Ajmera, Dhruv · 1 voice
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.CC #cs.DM #cs.DS #math.CO
paper · pdf · doi:10.48550/arxiv.2505.09628
arxiv published 2025/04/29 · arxiv updated 2025/05/16
A superpermutation is a sequence that contains every permutation of n distinct symbols as a contiguous substring. For instance, a valid example for three symbols 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 superpermutations directly and compactly. This improves memory usage, enabling the construction of larger sequences previously considered impractical.