indexTableau(YoungTableau) -- the index tableau for a given tableau

Synopsis

Function: indexTableau
Usage:

indexTableau(y)
Inputs:
- y, an instance of the type YoungTableau,
Outputs:
- an instance of the type YoungTableau, the index tableau

Description

The index tableau is a filling obtained by the original tableau using the reading word. To every element in the reading word a number is given recursively in the following way. f(0) = 0 and f(k+1) = f(k) if k+1 appear to the right of k. Otherwise f(k+1)= f(k)+1.

Finally the entries in the original tableau are replaced by the values of the function f.

i1 : p = new Partition from {3,2}

o1 = Partition{3, 2}

o1 : Partition

i2 : y = youngTableau(p,{0,2,3,1,4})

o2 = | 0 2 3 |
     | 1 4 |

o2 : YoungTableau

i3 : readingWord(y)

o3 = {1, 0, 4, 2, 3}

o3 : List

i4 : indexTableau(y)

o4 = | 0 1 1 |
     | 1 2 |

o4 : YoungTableau

Ways to use this method: