SYNOPSIS

lrcalc coprod [-a] part
lrcalc lrcoef outer - inner1 - inner2
lrcalc lrtab [-r rows] outer / inner
lrcalc mult [-mz] [-r rows] [-q rows,cols] [-f rows,level] part1 - part2
lrcalc skew [-m] [-r rows] outer / inner

coprod - Calculate coproducts in the ring of symmetric functions

DESCRIPTION

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.

OPTIONS

-a

not documented

EXAMPLE

% 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)

lrcoef - Compute a single Littlewood-Richardson coefficient

DESCRIPTION

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.

EXAMPLE

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

lrtab

not documented

mult - Expand a product of two Schur functions in the basis of Schur functions

DESCRIPTION

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.

OPTIONS

-mz

not documented

-r rows

not documented

-q rows,cols

Calculates quantum coefficients. Experimental feature.

-f rows,level

Calculates fusion coefficients. Experimental feature.

EXAMPLES

% 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)

skew - Expand a skew Schur function in the basis of Schur functions

DESCRIPTION

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.

OPTIONS

-m

not documented

-r rows

not documented

EXAMPLE

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

AUTHOR

Anders S. Buch <asbuch at math rutgers edu>

MANPAGE AUTHOR

Tobias Hansen <thansen at debian dot org>