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