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arXiv · 2104.02999

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

Gal Amram·Amir Rubin·Gera Weiss
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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.

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Gal Amram, Amir Rubin, Gera Weiss. 2021-04-07. A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence. https://arxiv.org/abs/2104.02999

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