BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-73-340
       ENTRY:: September 25, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Notes on a problem involving permutations as subsequences.
        TYPE:: Technical Report
      AUTHOR:: Newey, Malcolm C.
        DATE:: March 1973
       PAGES:: 22
    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. This paper catalogs some of the easy observations on
               the problem and proves that the minimum lengths for n=5, n=6
               & n=7 are 19, 28 and 39 respectively. Also presented is a
               construction which yields (for n>2) many appropriate
               sequences of length $n^2$-2n+4 so giving an upper bound on
               length of minimum strings which matches exactly all known
               values.
       NOTES:: [Adminitrivia V1/Prg/19950925]
         END:: STAN//CS-TR-73-340