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The Grandmama de Bruijn Sequence for Binary Strings

  • Patrick Baxter Dragon
  • Oscar I. Hernandez
  • Aaron WilliamsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

Abstract

A de Bruijn sequence is a binary string of length \(2^n\) 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.

Keywords

de Bruijn sequence Lexicographic order Necklace Lyndon word FKM construction Ford sequence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Patrick Baxter Dragon
    • 1
  • Oscar I. Hernandez
    • 1
  • Aaron Williams
    • 1
    Email author
  1. 1.Division of Science, Math and ComputingBard College at Simon’s RockGreat BarringtonUSA

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