COMMENT:
	KOSTKA
	------

NAME:
	allkostka
SYNOPSIS:
	INT allkostka(OP n)
DESCRIPTION:
	print all Kostka tables up to the INTEGER object n


NAME:
	kostka_number
SYNOPSIS:
	INT kostka_number(OP content,shape,result)
DESCRIPTION:
	computes the Kostka number, i.e. the number of
         tableaux of given shape, which is a PARTITION object, and
         of given content, which also is a PARTITION object, or a VECTOR
	object with INTEGER entries. The
         result is an INTEGER object, which is freed to an empty
         object at the beginning. The shape could also be a
         SKEWPARTITION object, then we compute the number of
         skewtableaux of the given shape.
BUGS:
	      The result is limited to INTEGER objects


NAME:
	     kostka_tab
SYNOPSIS:
	   INT kostka_tab(OP shape, content, result)
DESCRIPTION:
	computes the list of tableaux of given shape
        and content. shape is a PARTITION object or a
        SKEWPARTITION object and
        content is a PARTITION object or a VECTOR object with
	INTEGER entries, the result becomes a
        LIST object whose entries are the computed TABLEAUX
	object.
BUG:
	content should also be allowed to be a VECTOR object
        of INTEGERS.
	call to kostka_number and kostka_tab have different syntax
RETURN:
	OK or ERROR

EXAMPLE:
	look at the following example, which computes all tableaux of
	given shape and content, stores them in a file and reads this
	 back from the file, and prints them


	#include <symmetrica.h>
	main()
	{
	OP a,b,c,d;
	FILE *fp1,*fp2;
	anfang();

	a=callocobject(); b=callocobject(); c=callocobject(); d=callocobject();

	fp1=fopen("xxx","w");
	scan(PARTITION,a); scan(PARTITION,d); kostka_tab(a,d,b);
	objectwrite(fp1,b);fclose(fp1);
	fp2=fopen("xxx","r");
	objectread(fp2,c); println(c);

	freeall(a); freeall(b); freeall(c); freeall(d);

	ende();
	}

NAME:
	kostka_tafel
SYNOPSIS:
	INT kostka_tafel(OP n, result)
DESCRIPTION:
	computes the Kostka table for the weight n , the
       result is a matrix in the object result.

NAME:
	make_n_transpositionmatrix
SYNOPSIS:
	INT make_n_transpositionmatrix(OP dim,mat)
DESCRIPTION:
	computes the transpositions matrix of given
       weight dim, the result is a MATRIX object mat, where the
       entries are INTEGER objects 0 or 1. The rows and columns
       are labeled by the partitions of the weight dim, and a
       1 is the entry if and olny if the row index equals the
       conjugate of the column index.

NAME:
	     stirling_second_number
SYNOPSIS:
	   INT stirling_second_number(OP n,k,result)
DESCRIPTION:
	computes the Stirling number of the second kind,
	i.e. the number of possibilities to fill n pieces into
        k boxes. The input must be two INTEGER objects n,k.
BUGS:
	      Very slow function, because it uses the scalar
	product of rows of the Kostka table.


EXAMPLE:
	#include <symmetrica.h>
	main()
	{
	OP a,b,c;
	anfang();
	a= callocobject(); b= callocobject(); c= callocobject();
	scan(INTEGER,a); scan(INTEGER,b);
	stirling_second_number(a,b,c);println(c);
	freeall(a);freeall(b); freeall(c);
	ende();
	}


NAME:
	test_kostka
SYNOPSIS:
	INT test_kostka()
DESCRIPTION:
	tests the implementation of the Kostka routines

