Notes on a Problem Involving Permutations as Subsequences

Abstract

The problem (attributed to R. M. Karp by Knuth is to describe the sequences of minimum length which contain, as subsequences, all the permutations of an alphabet of n symbols. The paper catalogs come of the easy observations on the problem and proves that the minimum lengths for n=5, n=6 and n=7 are 19, 28 and 39 respectively. Also presented is a construction which yields (for n>2) many appropriate sequences of length (n sup 2)-2n+4 so giving an upper bound on length of minimum strings which matches exactly all known values.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1973
Accession Number
AD0759714

Entities

People

  • Malcolm Newey

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Aeronautics
  • Algorithms
  • Alphabets
  • Artificial Intelligence
  • Computer Science
  • Computers
  • Construction
  • Contracts
  • Mathematics
  • Notation
  • Observation
  • Permutations
  • Procedures (Computers)
  • Schools
  • Sequences
  • Universities

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Graph Algorithms and Convex Optimization.