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On strings containing all subsets as substrings

โœ Scribed by Witold Lipski Jr.


Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
998 KB
Volume
21
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


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.


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A new bound on the length of the shortes
โœ Cai Mao-cheng ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 196 KB

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,