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A supersequence over a finite set is a sequence that contains as subsequenceall permutations of the set. This paper defines an infinite array of methods tocreate supersequences of decreasing lengths. This yields the shortest knownsupersequences over larger sets. It also provides the best resultsasymptotically. It is based on a general proof using a new property calledstrong completeness. The same technique also can be used to prove existingsupersequences which combines the old and new ones into an unified conceptualframework.

Skip Letters for Short Supersequence of All Permutations