Shorter strings containing all k - element permutations
نویسنده
چکیده
We consider the problem of finding short strings that contain all permutations of order k over an alphabet of size n, with k ≤ n. We show constructively that k(n− 2) + 3 is an upper bound on the length of shortest such strings, for n ≥ k ≥ 10. Consequently, for n ≥ 10, the shortest strings that contain all permutations of order n have length at most n− 2n+ 3. These two new upper bounds improve with one unit the previous known upper bounds.
منابع مشابه
Short strings containing all k-element permutations
We consider the problem of finding short strings that contain all permutations of order k over an alphabet of size n, with k ≤ n. We show constructively that k(n− 2) + 3 is an upper bound on the length of shortest such strings, for n ≥ k ≥ 10. Consequently, for n ≥ 10, the shortest strings that contain all permutations of order n have length at most n− 2n+ 3. These two new upper bounds improve ...
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تاریخ انتشار 2012