Containing All Permutations
نویسندگان
چکیده
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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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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Following [M2], let S (r) n be the set of all coloured permutations on the symbols 1, 2, . . . , n with colours 1, 2, . . . , r, which is the analogous of the symmetric group when r = 1, and the hyperoctahedral group when r = 2. Let I ⊆ {1, 2, . . . , r} be subset of d colours; we define T k,r(I) be the set of all coloured permutations φ ∈ S (r) k such that φ1 = m (c) where c ∈ I. We prove that...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2021
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2021.1835384