# bracket2partition -- dictionary between different notations for Schubert conditions.

## Synopsis

• Usage:
l = bracket2partition(b,n)
• Inputs:
• b, a list, of length $k$, a bracket representing a Schubert condition.
• n, an integer, $k$ and $n$ represent the Grassmannian $Gr(k,n)$
• Outputs:
• l, a list, the corresponding partition

## 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