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SG::Perm2Desc -- computes the list of descents of a permutation

Call(s)


SG::Perm2Desc(perm <,nb,maj,comaj>)

Parameters

perm- any list denoting a permutation
nb- only counts objects
maj- sum of descent positions
comaj- sum of all values

Introduction

The SG::Perm2Desc function computes the list of descents of the permutation perm, i.e. the list of positions i, such that perm[i] > perm[i+1].

When called with the second argument maj, it returns the sum of the descent positions.

When called with the second argument comaj, it returns the sum of all values (n - descent position), where n is equal to nops(perm).

Example 1

>> muEC::SG::Perm2Desc( [3,1,4,2,6,5,7] );
                                 [1, 3, 5]
>> muEC::SG::Perm2Desc( [3,1,4,2,6,5,7], nb );
                                     3
>> muEC::SG::Perm2Desc( [3,1,4,2,6,5,7], maj );
                                     9
>> muEC::SG::Perm2Desc( [3,1,4,2,6,5,7], comaj );
                                    12

Related Functions

Perm2Rise

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MuPAD Combinat, an open source algebraic combinatorics package