lrcalc - Calculate with Littlewood-Richardson coefficients

Author

       Anders S. Buch <asbuch at math rutgers edu>

Coprod - Calculate Coproducts In The Ring Of Symmetric Functions

DESCRIPTION
              The  command  "lrcalccoprodz"  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 "lrcalclrcoefz-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

Manpage Author

       Tobias Hansen <thansen at debian dot org>

Linux                                              AUGUST 2013                                         LRCALC(1)

Mult - Expand A Product Of Two Schur Functions In The Basis Of Schur Functions

DESCRIPTION
              The  command  "lrcalcmultx-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

              -rrows
                     not documented

              -qrows,cols
                     Calculates quantum coefficients. Experimental feature.

              -frows,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)

Name

       lrcalc - Calculate with Littlewood-Richardson coefficients

Skew - Expand A Skew Schur Function In The Basis Of Schur Functions

DESCRIPTION
              The command "lrcalcskewz/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

              -rrows
                     not documented
       EXAMPLE
              % lrcalc skew 3 2 1 / 2 1
              1  (3)
              2  (2, 1)
              1  (1, 1, 1)

Synopsis

lrcalccoprod [-a] partlrcalclrcoefouter-inner1-inner2lrcalclrtab [-rrows] outer/innerlrcalcmult [-mz] [-rrows] [-qrows,cols] [-frows,level] part1-part2lrcalcskew [-m] [-rrows] outer/inner