# 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