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A121981 Number of finite maximal bifix codes of degree n on a two-letter alphabet.

Original entry on oeis.org

1, 1, 3, 73, 5056783
Offset: 1

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Author

Alessandro De Luca, Feb 09 2011

Keywords

Comments

A bifix (sometimes biprefix) code is a set of nonempty words X such that no word of X is a proper prefix or a proper suffix of another. The degree of a finite maximal bifix code X is the maximal number of parses that a word can have with respect to X.
It is known that there are finitely many finite maximal bifix codes of each degree.

Examples

			On the alphabet {a,b}, for n=3 the a(3)=3 codes are:
{aaa,aab,aba,abb,baa,bab,bba,bbb},
{aaa,aaba,aabb,ab,baa,baba,babb,bba,bbb},
{aaa,aab,abaa,abab,abb,ba,bbaa,bbab,bbb}

References

  • J. Berstel and D. Perrin, Theory of Codes, Academic Press, 1985, Chapter III.

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