Jeu de taquin, Lehmer code Tableaux Building and making Words, rows, columns, content, shape

Words, rows, columns, content, shape

With every tableau or skewtableau you have an associated word, which you get if you read the entries in a certain order. The default word is the row word: The evaluation of the row word: The evaluation of the column word:
Example: Here is an example:
...
scan(TABLEAUX,a); println(a);
wordoftableaux(a,b);println(b);
rowwordoftableaux(a,c);println(c);
columnwordoftableaux(a,d);println(d);
...
In case you enter the tableau

5 6 7

1 2 3 4

the output will look as follows:

5 6 7

1 2 3 4

[4,3,2,1,7,6,5]

[4,3,2,1,7,6,5]

[5,1,6,2,7,3,4]

Please note that wordoftableaux also gives the row word of the tableau, it is simply the default value.

In order to access the rows and columns of the tableaux, we have routines which give you the last and first index of the entries:

The index of the last entry in a column: The index of the first entry of a row: The index of the last entry in a row: An interesting routine is the one that computes the content of a tableau, i.e. the number of entries of each type, it is an integer vector, where the first entry is the number of 1's in the tableau the second entry is the number of 2's and so on. For a given MATRIX which is a tableau, we can compute the shape (umriss)
harald.fripertinger "at" uni-graz.at, May 26, 2011

Jeu de taquin, Lehmer code Tableaux Building and making Uni-Graz Mathematik Words, rows, columns, content, shape Valid HTML 4.0 Transitional Valid CSS!