A de Bruijn sequence is a binary string of length 2n which, when viewed cyclically, contains every binary string of length n exactly once as a substring. Knuth refers to the lexicographically least de Bruijn sequence for each n as the “granddaddy” and Fredricksen et al. showed that it can be constructed by concatenating the aperiodic prefixes of the binary necklaces of length n in lexicographic order. In this paper we prove that the granddaddy has a lexicographic partner. The “grandmama” sequence is constructed by instead concatenating the aperiodic prefixes in co-lexicographic order. We explain how our sequence differs from the previous sequence and why it had not previously been discovered.
CITATION STYLE
Dragon, P. B., Hernandez, O. I., & Williams, A. (2016). The grandmama de bruijn sequence for binary strings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9644, pp. 347–361). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_26
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