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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