A Schubert condition in the Grassmannian $Gr(k,n)$ is encoded either by a partition $l$ or by a bracket $b$.
A partition is a weakly decreasing list of at most $k$ nonnegative integers less than or equal to $n-k$. It may be padded with zeroes to be of length $k$.
A bracket is a strictly increasing list of length $k$ of positive integers between $1$ and $n$.
This function writes a partition as a bracket. They are related as follows $b_{k+1-i}=n-i-l_i$, for $i=1,...,k$.
i1 : l = {2,1}; |
i2 : k = 2; |
i3 : n = 4; |
i4 : partition2bracket(l,k,n) o4 = {1, 3} o4 : List |
i5 : k = 3; |
i6 : n = 6; |
i7 : partition2bracket(l,k,n) o7 = {2, 4, 6} o7 : List |
The object partition2bracket is a method function.