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.

中文翻译：

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Prefer-Max De Bruijn序列的循环连接构造

基于循环连接技术，我们提出了一种新颖的构造，用于众所周知的prefer-max De Bruijn序列。我们进一步表明，该构造以直接的方式暗示了文献中的已知结果。首先，它暗示了洋葱定理的正确性，指出实际上，prefer-max的逆实际上是一个无限的De Bruijn序列。其次，它暗示了最近发现的偏好最大值，偏好最小值及其反转的移位规则的正确性。最后，它构成了开创性FKM定理的另一种证明。