with 
. muEC::TYP::IsPerm – tests for permutations
tests whether the argument is a permutation
Call:
muEC::TYP::IsPerm(expr, <dominant | grassmannian | vexillary>)
Parameters:
|
expr: |
any expression |
Related Functions:
Details:
The muEC::TYP::IsPerm function tests whether expr is a permutation that is a list of n disctinct positive integers between 1 and n.
One can test whether the permutation is either dominant, grassmannian or vexillary by using the corresponding second argument, dominant, grassmannian or vexillary.
A permutation is dominant, if and only if its code is a partition (i.e. weakly decreasing vector of non-negative integers).
A permutation is grassmannian, if and only if it has only one descent, or in other words, if there exists only one with .
Let part(perm) be the partition obtained by reordering the components of its code. Then perm is vexillary if and only if part(Perm2Inv(perm)) is the conjugate of part(perm).
muEC::TYP::IsPerm( [3,1] );
muEC::TYP::IsPerm( [3,2,1] );
muEC::TYP::IsPerm( [2,1,4,3], vexillary );
