The command "lrcalc coprod z" lists all pairs of partitions x and y for which the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, with that coefficient in front.

-a

not documented

% lrcalc coprod 3 2 1
1 (3, 1) (2)
1 (2, 2) (1, 1)
1 (3, 1) (1, 1)
1 (2, 1) (3)
2 (2, 1) (2, 1)
1 (2, 2, 1) (1)
1 (3, 2, 1) ()
1 (3, 2) (1)
1 (2, 1, 1) (2)
1 (3, 1, 1) (1)
1 (1, 1, 1) (2, 1)
1 (2, 1, 1) (1, 1)
1 (2, 2) (2)

The command "lrcalc lrcoef z - x - y" computes the Littlewood-Richardson coefficient c^z_{x,y} which is the coefficient of the Schur function s_z in the product s_x * s_y.

% lrcalc lrcoef 3 2 1 - 2 1 - 2 1
2

The command "lrcalc mult x - y" lists all partitions z for which the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, with that coefficient in front.

-mz

not documented

-r rows

not documented

-q rows,cols

Calculates quantum coefficients. Experimental feature.

-f rows,level

Calculates fusion coefficients. Experimental feature.

% lrcalc mult 2 1 - 2 1
1 (3, 3)
1 (4, 2)
1 (2, 2, 1, 1)
1 (2, 2, 2)
2 (3, 2, 1)
1 (4, 1, 1)
1 (3, 1, 1, 1)

% lrcalc mult -f 3,2 3 2 1 - 3 2 1
1 (4, 4, 4)
1 (5, 4, 3)

% lrcalc mult -q 3,2 3 2 1 - 3 2 1
1 (2)
1 (1, 1)

The command "lrcalc skew z / x" lists all partitions y for which the Littlewood-Richardson coefficient c^z_{x,y} is non-zero, with that coefficient in front.

-m

not documented

-r rows

not documented

% lrcalc skew 3 2 1 / 2 1
1 (3)
2 (2, 1)
1 (1, 1, 1)