The purpose of this note is to give a new upper bound of the shortest string containing all r-permutations. Thus we disprove the conjecture considered in Cl]. The terminology used in this note fullows [I]. Koutas and Nu [I] proposed the foIlowing problem of constructing a shortest string of (1, 2,
Shortest string containing all permutations
โ Scribed by P.J. Koutas; T.C. Hu
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 1007 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
Revkd t 7 M
๐ SIMILAR VOLUMES
Given n and k, we consider the problem of conslructing a shortest string over the, set ~. ={1,2 ..... n} which contains every permulation of each k-element subset of ~, as a scbsequence. Let g(n, k) denote the length of a shorte,;t such string. We show by construction tic, a: g(n, k) <~ k(n -2) + 4
Let s,, be the length of a shortest sequence cf positive integers which contains every Yc(l,..., d}-as a subsequence of IY 1 consecutive terms. We give the following asymptotic estimation\* (2/7rnY22" d S . n Q (2/7r)2". TIC. upper bound is derived constructively.