partition2bracket -- dictionary between different notations for Schubert conditions.

Synopsis

Usage:

b = partition2bracket(l,k,n)
Inputs:
- l, a list, partition representing a Schubert condition
- k, an integer,
- n, an integer, $k$ and $n$ represent the Grassmannian $Gr(k,n)$
Outputs:
- b, a list, the corresponding bracket

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

Ways to use partition2bracket :

partition2bracket(List,ZZ,ZZ)

For the programmer

The object partition2bracket is a method function.

partition2bracket -- dictionary between different notations for Schubert conditions.

Synopsis

Description

See also

Ways to use partition2bracket :

For the programmer