Combinatorics |

Their table, and also the table of the Stirling numbers of the first kind, can be evaluated bystirling_second_number()

These routines provide the upper left hand corner of prescribed number of rows and columns. The Kostka numbers are of course there:stirling_first_tafel(), stirling_second_tafel().

as well as their table:kostka_number()

Moreover, there are, as it was already mentioned, several tables and values of characters available, for symmetric groups, alternating groups and wreath products of symmetric groups, see the appropriate documentation files. This part of the program system is of course in rapid progress.kostka_tafel().

An important part of the combinatorics used in the representation theory of symmetric groups can be formulated in terms of tableaux.

Please note that the standard Young tableaux are the tableaux of contentExample:Here is a routine that allows to construct all the tableaux of prescribed content (cf.ex19.c):... scan(PARTITION,a); println(a); scan(PARTITION,b); println(b); kostka\_tab(a,b,c);println(c); ...Here is the output which you obtain according to the input of the partitions23and11111of 5:23

11111

4 5

1 2 3

3 5

1 2 4

3 4

1 2 5

2 5

1 3 4

2 4

1 3 5

There are also routines that give this row word or the column word of skew tableaux.

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001

Combinatorics |