# lrcalc - Online in the Cloud

This is the command lrcalc that can be run in the OnWorks free hosting provider using one of our multiple free online workstations such as Ubuntu Online, Fedora Online, Windows online emulator or MAC OS online emulator

### PROGRAM:

#### 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-Calculatecoproductsintheringofsymmetricfunctions

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-ComputeasingleLittlewood-Richardsoncoefficient

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

not documented

#### mult-ExpandaproductoftwoSchurfunctionsinthebasisofSchurfunctions

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)

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)

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