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## `TYP::IsPerm` -- tests whether the argument is a permutation

#### Call(s)

`TYP::IsPerm(expr <,dominant,grassmannian,vexillary>)`

#### Parameters

`expr` | - | any expression

#### Introduction

The `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 Functions

`Permutation`

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MuPAD Combinat, an open source algebraic combinatorics package