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- W2047385961 abstract "A set of words {A 1 , A 2 , …, A t } can be independently prescribed if for every set of t nonnegative integers ν i ( i = 1, 2, …, t ), there exists a word S containing exactly ν i occurrences of A i ( i = 1, 2, …, t ). In this paper we consider n -letter sets of independently prescribable words, where an n -letter set is a set of n -letter words. We show that the maximum size for an independently prescribable n -letter set is q n − q n −1 , where q is the number of letters in the alphabet (assuming q > 2 or n > 2). An independently prescribable n -letter set J such that | J | = q n − q n −1 can be constructed in the following way: Let D be an ( n − 1)- de Bruijn sequence , a circular sequence with exactly one occurrence of every ( n − 1)-letter word froom a q -letter alphabet. Then an independently prescribable n -letter set with cardinality q n − q n −1 consists of all n -letter words except those occurring in D . We show that each de Bruijn sequence corresponds to a unique independently prescribable n -letter set J such that | J | = q n − q n −1 . If q > 2, the number of such sets is the number of ( n − 1)-de Bruijn sequences (( n , q ) ≠ (2, 3)). If q = 2 and n ⩾ 5, the number of such sets is 7 times the number of ( n − 1)-de Bruijn sequences. Some of the results in this paper are generalized in a theorem about independently prescribable sets of edges of Hamiltonian graphs." @default.
- W2047385961 created "2016-06-24" @default.
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- W2047385961 date "1984-01-01" @default.
- W2047385961 modified "2023-09-29" @default.
- W2047385961 title "Independently prescriable sets of n-letter words" @default.
- W2047385961 cites W2019338982 @default.
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- W2047385961 doi "https://doi.org/10.1016/0012-365x(84)90048-7" @default.
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