chap7.txt

  
  7 Some Permutation Essentials
  
  In  this  chapter  we  mention  a couple functions that are fairly basic but
  useful tools to work with.
  
  
  7.1 Complement
  
  7.1-1 PermComplement
  
  PermComplement( perm )  function
  Returns:  The permutation that is the complement of perm.
  
  The complement of a permutation τ=τ_1...τ_n is the permutation
  
  
  τ^C=(n+1)-τ_1 (n+1)-τ_2... (n+1)-τ_n
  
  .
  
    Example  
    gap> PermComplement([3,2,8,6,7,1,5,4]);
    [ 6, 7, 1, 3, 2, 8, 4, 5 ]
    gap> 
  
  
  
  7.2 Rank Encoding
  
  7.2-1 IsRankEncoding
  
  IsRankEncoding( perm )  function
  Returns:  true if perm is a valid rank encoding of a permutation.
  
  IsRankEncoding  checkes whether the input list perm is a valid rank encoding
  by  checking whether it is accepted by the bounded class automaton, with the
  highest rank being set by the highest element in perm.
  
    Example  
    gap> IsRankEncoding([3,2,6,4,4,1,2,1]);
    true
    gap> IsRankEncoding([3,2,6,4,5,1,2,1]);
    false
    gap>