We present a simple greedy algorithm to construct the prefer-same de Bruijn sequence and prove that it is equivalent to the more complex algorithm first stated by Eldert et al. without proof (Eldert et al., 1958 [3]), and later by Fredricksen (Fredricksen, 1982 [5]). Then we prove that the resulting sequence has the lexicographically largest run-length representation among all de Bruijn sequences. Furthermore, we prove that the sequence resulting from a prefer-opposite greedy construction has the lexicographically smallest run-length representation among all de Bruijn sequences.

中文翻译：

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重新审视布鲁姆序列的相同和相对优先

我们提出了一个简单的贪心算法来构建相同优先的de Bruijn序列，并证明它等效于Eldert等人首先提出的更复杂的算法。（Eldert et al。，1958 [3]），后来又由Fredricksen（Fredricksen，1982 [5]）提出。然后，我们证明了所得序列在所有de Bruijn序列中具有按字典顺序的最大游程长度表示。此外，我们证明了由偏好相反的贪婪构造产生的序列在所有de Bruijn序列中具有字典上最小的游程长度表示。