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:
• NAME: wordoftableaux
• SYNOPSIS: INT wordoftableaux(OP a,b)
The evaluation of the row word:
• NAME: rowwordoftableaux
• SYNOPSIS: INT rowwordoftableaux(OP a,b)
The evaluation of the column word:
• NAME: columnwordoftableaux
• SYNOPSIS: INT columnwordoftableaux(OP a,b)
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:

• NAME: spaltenanfang
• SYNOPSIS: INT spaltenanfang(OP a, INT b)
• DESCRIPTION: returns the row number of the first entry in the column labeled by b. If b is a index which is too big it returns the value of s_t_hi(a).
• ERROR: if b is negative you get an error
The index of the last entry in a column:
• NAME: spaltenende
• SYNOPSIS: INT spaltenende(OP a, INT b)
• DESCRIPTION: returns the row number of the last entry in the column labeled by b. If b is an index which is too big it returns -1L
• ERROR: if b is negative you get an error
The index of the first entry of a row:
• NAME: zeilenanfang
• SYNOPSIS: INT zeilenanfang(OP a, INT b)
• DESCRIPTION: returns the column number of the first entry in the row labeled by b. If b is an index which is too big it returns the value of s_t_li(a).
• ERROR: if b is negative you get an error
The index of the last entry in a row:
• NAME: zeilenende
• SYNOPSIS: INT zeilenende(OP a, INT b)
• DESCRIPTION: returns the column number of the last entry in the row labeled by b. If b is an index which is too big it returns -1L
• ERROR: if b is negative you get an error
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.
• NAME: inhalt_tableau
• SYNOPOSIS: INT inhalt_tableau(OP a,b)
For a given MATRIX which is a tableau, we can compute the shape (umriss)
• NAME: m_matrix_umriss
• SYNOPSIS: INT m_matrix_umriss(OP a,b)

harald.fripertinger@kfunigraz.ac.at,
last changed: November 19, 2001

 Words, rows, columns, content, shape