A Schubert problem in the Grassmannian $Gr(k,n)$ is encoded by either a list of partitions or brackets whose codimensions sum to $k(n-k)$. (see bracket2partition for details on brackets and partitions)
The PHCPack implementations of the geometric Littlewood-Richardson rule encode the brackets in a matrix, where each row has the form ${m, b}$ with $m$ the multiplicity of the bracket $b$, which is a strictly increasing sequence of $k$ integers between $1$ and $n$.
i1 : k=4; |
i2 : n = 8; |
i3 : SchubProbP = {{2,2},{2,2},{2,2},{1},{1},{1},{1}} o3 = {{2, 2}, {2, 2}, {2, 2}, {1}, {1}, {1}, {1}} o3 : List |
i4 : NSC2phc(SchubProbP,k,n) o4 = | 3 3 4 7 8 | | 4 4 6 7 8 | 2 5 o4 : Matrix ZZ <--- ZZ |
i5 : k=4; |
i6 : n = 8; |
i7 : SchubProbB = {{3,4,7,8},{3,4,7,8},{3,4,7,8},{4,6,7,8},{4,6,7,8},{4,6,7,8},{4,6,7,8}} o7 = {{3, 4, 7, 8}, {3, 4, 7, 8}, {3, 4, 7, 8}, {4, 6, 7, 8}, {4, 6, 7, 8}, ------------------------------------------------------------------------ {4, 6, 7, 8}, {4, 6, 7, 8}} o7 : List |
i8 : NSC2phc(SchubProbB,4,8) o8 = | 3 3 4 7 8 | | 4 4 6 7 8 | 2 5 o8 : Matrix ZZ <--- ZZ |
The object NSC2phc is a method function.