Skip Letters for Short Supersequence of All Permutations

TL;DR

This paper introduces a novel array of methods to construct minimal supersequences containing all permutations, achieving the shortest known sequences and optimal asymptotic results through a new property called strong completeness.

Contribution

It presents a new framework for constructing shortest supersequences of all permutations using the concept of strong completeness, unifying existing methods and improving length bounds.

Findings

Shortest known supersequences over larger sets

Asymptotically optimal supersequence lengths

Unified framework for existing supersequence constructions

Abstract

A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known supersequences over larger sets. It also provides the best results asymptotically. It is based on a general proof using a new property called strong completeness. The same technique also can be used to prove existing supersequences which combines the old and new ones into an unified conceptual framework.