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NumericalSchubertCalculus :: partition2bracket

partition2bracket -- dictionary between different notations for Schubert conditions.

Synopsis

Description

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

See also

Ways to use partition2bracket :

For the programmer

The object partition2bracket is a method function.