A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

Gal Amram, Amir Rubin, Gera Weiss

Research output: Working paper/PreprintPreprint

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Abstract

We propose a novel construction for the well-known prefer-max De Bruijn sequence, based on the cycle joining technique. We further show that the construction implies known results from the literature in a straightforward manner. First, it implies the correctness of the onion theorem, stating that, effectively, the reverse of prefer-max is in fact an infinite De Bruijn sequence. Second, it implies the correctness of recently discovered shift rules for prefer-max, prefer-min, and their reversals. Lastly, it forms an alternative proof for the seminal FKM-theorem.
Original languageEnglish
Number of pages12
StatePublished - 2021

Keywords

  • cs.DM
  • math.CO

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