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 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  "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

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 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)

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 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)

AUTHOR

       Anders S. Buch <asbuch at math rutgers edu>

MANPAGE AUTHOR

       Tobias Hansen <thansen at debian dot org>