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De Bruijn Sequences: From Games to Shift-Rules to a Proof of the Fredricksen-Kessler-Maiorana Theorem (1805.02405v3)
Published 7 May 2018 in cs.DM and math.CO
Abstract: We present a combinatorial game and propose efficiently computable optimal strategies. We then show how these strategies can be translated to efficiently computable shift-rules for the well known prefer-max and prefer-min De Bruijn sequences, in both forward and backward directions. Using these shift-rules, we provide a new proof of the well known theorem by Fredricksen, Kessler, and Maiorana on De Bruijn sequences and Lyndon words.