TYP::IsPerm --
tests whether the argument is a permutation
Call(s)
TYP::IsPerm(expr <,dominant,grassmannian,vexillary>)
Parametersexpr | - | any expression |
IntroductionThe 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 i with perm[i]>perm[i+1].
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).
Example 1>> muEC::TYP::IsPerm( [3,1] );
FALSE
>> muEC::TYP::IsPerm( [3,2,1] );
TRUE
>> muEC::TYP::IsPerm( [2,1,4,3], vexillary );
FALSE
Related FunctionsMuPAD Combinat, an open source algebraic combinatorics package