FUNCTION: Perm2Rothe - calculate the Rothe diagram of a permutation

CALLING SEQUENCE:

Perm2Rothe(perm)

SG[Perm2Rothe](perm)

PARAMETERS:

perm = any list denoting a permutation

SYNOPSIS:

• The Perm2Rothe function calculates the Rothe diagram of a permutation. The boxes of the diagram are numbered by consecutive numbers, starting from the row number.

• The matrix of the x's is the matrix representing the permutation.

• Reading the entries from right to left and top to bottom, one obtains a canonical reduced decomposition of the permutation (i stands for the simple transposition exchanging i and i+1).

• Whenever there is a conflict between the function name Perm2Rothe and another name used in the same session, use the long form SG['Perm2Rothe'].

EXAMPLES:

> with(SG):
> Perm2Rothe([6,1,4,5,3,2]);
 
                              [ 1  2  3  4  5  x ]
                              [                  ]
                              [ x  .  .  .  .  . ]
                              [                  ]
                              [ .  3  4  x  .  . ]
                              [                  ]
                              [ .  4  5  .  x  . ]
                              [                  ]
                              [ .  5  x  .  .  . ]
                              [                  ]
                              [ .  x  .  .  .  . ]
 
> Perm2Rd([6,1,4,5,3,2]);
 
                         [5, 4, 3, 2, 1, 4, 3, 5, 4, 5]