TY - UNPB

T1 - A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

AU - Amram, Gal

AU - Rubin, Amir

AU - Weiss, Gera

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - cs.DM

KW - math.CO

M3 - Preprint

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

ER -