我们调查用操作的一个特殊的类列出联合的问题,前缀移动。联合作为 0 和 1 的位串被代表,并且前缀移动是旋转的操作由一个位置到的一点绳的某前缀左或正确。我们把一个否定答案给 F 问的一个开的问题。Ruskey 和威廉斯·阿(由前缀移动产生联合,在 Proc。 第11 年度国际计算和组合数学会议 2005 , LNCS 3595 , Springer , 2005 , pp.570 576 ),那是我们是否能由仅仅在位串上使用三很基本的前缀移动产生联合,它是开始的二位和由在任何一个方向的一个位置的全部位串的旋转的调换(即,使用排列 σ2 ,σ n 和σ n ? 1 到位串的索引)。电子增补材料这篇文章(doi:10.1007/s11390-007-9094-7 ) 的联机版本包含增补材料,它对授权用户可得到。
We investigate the problem of listing combinations using a special class of operations, prefix shifts. Combinations are represented as bitstrings of O's and l's, and prefix shifts are the operations of rotating some prefix of a bitstring by one position to left or right. We give a negative answer to an open problem asked by F. Ruskey and A. Williams (Generating combinations by prefix shifts, In Proc. llth Annual International Computing and Combinatorics Conference 2005, LNCS 3595, Springer, 2005, pp.570-576), that is whether we can generate combinations by only using three very basic prefix shifts on bitstrings, which are transposition of the first two bits and the rotation of the entire bitstring by one position in either direction (i.e., applying the permutations σ2, σn and σn^-1 to the indices of the bitstrings).