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

Ways to use bracket2partition :

bracket2partition(List,ZZ)

For the programmer

The object bracket2partition is a method function.

bracket2partition -- dictionary between different notations for Schubert conditions.

Synopsis

Description

See also

Ways to use bracket2partition :

For the programmer