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- W2157399833 abstract "A (non-circular) de Bruijn sequence w of order n is a word such that every word of length n appears exactly once in w as a factor. In this paper, we generalize the concept to a multi-shift setting: a multi-shift de Bruijn sequence tau(m,n) of shift m and order n is a word such that every word of length n appears exactly once in w as a factor that starts at index im+1 for some integer i>=0. We show the number of the multi-shift de Bruijn sequence tau(m,n) is (a^n)!a^{(m-n)(a^n-1)} for 1<=n<=m and is (a^m!)^{a^{n-m}} for 1<=m<=n, where a=|Sigma|. We provide two algorithms for generating a tau(m,n). The multi-shift de Bruijn sequence is important in solving the Frobenius problem in a free monoid." @default.
- W2157399833 created "2016-06-24" @default.
- W2157399833 creator A5036475829 @default.
- W2157399833 date "2010-04-08" @default.
- W2157399833 modified "2023-09-27" @default.
- W2157399833 title "Multi-Shift de Bruijn Sequence" @default.
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