schur.sagews

s = SymmetricFunctions(QQ).s()
import sage.libs.lrcalc.lrcalc as lrcalc
from sage.libs.lrcalc.lrcalc import lrskew
def pp(a,b):
    for c in (s(a)*s(b)).support():
        for st in lrskew(c,a,weight=b):
            st.pp()
pp([2,1],[1])

. . 1 . . . . 1 . . . 1

lrcalc.lrcoef([3,1,1],[1,1],[1])

0

for i in lrskew([8, 8, 5, 5, 4, 3, 3, 3, 2, 1], [7,5,3,2,1,1],weight=[6,6,5,4,2]):
    i.pp()

. . . . . . . 1 . . . . . 1 1 2 . . . 2 2 . . 1 3 3 . 1 2 4 . 2 3 1 3 4 2 4 5 3 5 4

for i in lrskew([8, 8, 5, 5, 4, 3, 3, 3, 2, 1], [6,5,3,2,1],weight=[7,6,5,4,2,1]):
    i.pp()

. . . . . . 1 1 . . . . . 1 2 2 . . . 1 2 . . 1 3 3 . 1 2 4 1 2 3 2 3 4 3 4 5 4 5 6 . . . . . . 1 1 . . . . . 1 2 2 . . . 1 2 . . 1 3 3 . 1 2 4 1 2 3 2 3 4 3 4 5 4 6 5 . . . . . . 1 1 . . . . . 1 2 2 . . . 1 3 . . 1 2 4 . 1 2 3 1 2 3 2 3 4 3 4 5 4 5 6 . . . . . . 1 1 . . . . . 1 2 2 . . . 1 3 . . 1 2 4 . 1 2 3 1 2 3 2 3 4 3 4 5 4 6 5

for i in lrskew([9,5,4,1,1],[5,2,1,1],weight=[4,4,3]):
    i.pp()

. . . . . 1 1 1 1 . . 2 2 2 . 2 3 3 . 3 . . . . . 1 1 1 1 . . 2 2 2 . 3 3 3 . 2

for i in lrskew([9,5,4,1,1],[4,2,1],weight=[5,4,3,1]):
    i.pp()

. . . . 1 1 1 1 1 . . 2 2 2 . 2 3 3 3 4 . . . . 1 1 1 1 1 . . 2 2 2 . 3 3 3 2 4

p=PlanePartition([[4,3,3,1],[3,1],[2,1]])
show(p)

show(PlanePartition([[3,2,1],[3,2],[3,1]]))

P = PlanePartitions((5,4,4))
show(P.random_element())

P = PlanePartitions((5,4,4))
show(P.random_element())