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NumericalSchubertCalculus :: bracket2partition

bracket2partition -- 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 bracket as a partition. They are related as follows $b_{k+1-i}=n-i-l_i$, for $i=1,...,k$.

i1 : b = {1,3};
i2 : n = 4;
i3 : bracket2partition(b,n)

o3 = {2, 1}

o3 : List
i4 : n = 6;
i5 : bracket2partition(b,n)

o5 = {4, 3}

o5 : List
i6 : b = {2,4,6};
i7 : bracket2partition(b,n)

o7 = {2, 1, 0}

o7 : List

See also

Ways to use bracket2partition :

For the programmer

The object bracket2partition is a method function.