On 4/17/07, James Propp <propp@math.wisc.edu> wrote:
Fred Lunnon writes:
Even if the following were to work, it would hardly qualify as an "explicit" construction: but for what it's worth, suppose we have already to hand a (cyclic) deBruijn sequence S_n in which every binary word of length n occurs as a factor exactly once.
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A very nice idea! Can it be taken out to infinity?
A complete search yielded the following maximal sequence, with n = 7 : [01011001001101110001010100101111 00111011010000100011001100001101 01011101001111011111000001011011 00011100101000100100000001111111] For n >= 7, it looks as if no span-n binary deBruijn sequence with factor 0^n1^n can be extended to one of span n+1, even if the "bad" factor is replaced by 0^{n+1}1^{n+1}. WFL