Man page - lrcalc(1)
Packages contains this manual
Manual
LRCALC
NAMESYNOPSIS
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>