table of contents
- 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
LRCALC(1) | User Manuals | LRCALC(1) |
NAME¶
lrcalc - Calculate with Littlewood-Richardson coefficientsSYNOPSIS¶
lrcalc coprod [-a] partlrcalc 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¶
DESCRIPTIONThe 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
% 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)
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¶
DESCRIPTIONThe 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
2
lrtab¶
not documentedmult - Expand a product of two Schur functions in the basis of Schur functions¶
DESCRIPTIONThe 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.
% 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)
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¶
DESCRIPTIONThe 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
% lrcalc skew 3 2 1 / 2 1
1 (3)
2 (2, 1)
1 (1, 1, 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>AUGUST 2013 | Linux |