Man page - lrcalc(1)

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Manual

LRCALC

NAME
SYNOPSIS
coprod - Calculate coproducts in the ring of symmetric functions
lrcoef - Compute a single Littlewood-Richardson coefficient
lrtab
mult - Expand a product of two Schur functions in the basis of Schur functions
skew - Expand a skew Schur function in the basis of Schur functions
AUTHOR
MANPAGE AUTHOR

NAME

lrcalc - Calculate with Littlewood-Richardson coefficients

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 cˆz_{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 cˆz_{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 cˆz_{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 cˆz_{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>