On a combinatorial generation problem of Knuth

@article{Merino2020OnAC,
  title={On a combinatorial generation problem of Knuth},
  author={Arturo I. Merino and Ondrej Micka and Torsten M{\"u}tze},
  journal={SIAM J. Comput.},
  year={2020},
  volume={51},
  pages={379-423}
}
The well-known middle levels conjecture asserts that for every integer $n\geq 1$, all binary strings of length $2(n+1)$ with exactly $n+1$ many 0s and 1s can be ordered cyclically so that any two consecutive strings differ in swapping the first bit with a complementary bit at some later position. In his book `The Art of Computer Programming Vol. 4A' Knuth raised a stronger form of this conjecture (Problem 56 in Section 2.1.3, Chapter 7), which requires that the sequence of positions with which… 

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