TY - UNPB
T1 - A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence
AU - Amram, Gal
AU - Rubin, Amir
AU - Weiss, Gera
PY - 2021/4/7
Y1 - 2021/4/7
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
U2 - 10.48550/arXiv.2104.02999
DO - 10.48550/arXiv.2104.02999
M3 - Preprint
BT - A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence
ER -