title: Finding completely dissimilar permutations
body: <p>For a sequence of n distinct elements, like for example {0, 1, 2, ..., n-1}, where n is even, it is possible to identify n permutations of the sequence that are completely dissimilar from each other. If n is odd, then it is possible to identify n-1 such permutations. Note, this is just a claim and not yet a fact.</p>
  
  <p>By completely dissimilar (which might not be accurate), I mean that there is no "adjacent and ordered pair" of elements, like (0,1), (2,3) and (n-3, n-2), from a certain permutation that repeats in any of the remaining permutations.</p>
  
  <p>For example:</p>
  
  <p>If n=2, then we can identify {0, 1} and {1, 0} as two completely dissimilar permutations.</p>
  
  <p>If n=3, then we can identify {0, 1, 2} and {2, 1, 0} as two completely dissimilar permutations.</p>
  
  <p>If n=4, then we can identify {0, 1, 2, 3}, {1, 3, 0, 2}, {2, 0, 3, 1} and {3, 2, 1, 0} as four completely dissimilar permutations.</p>
  
  <p>If n=5, then we can identify {0, 1, 2, 3, 4}, {1, 4, 2, 0, 3}, {3, 0, 2, 4, 1}, {4, 3, 2, 1, 0} as four completely dissimilar permutations.</p>
  
  <p>I will like to know:</p>
  
  <p>1) Is there a general rule or algorithm to find, given a sequence, any n (if n is even) or n-1 (if n is odd) completely dissimilar permutations of that sequence?</p>
  
  <p>2) Is there a formal definition of this problem?</p>