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PART::ListPart -- list of partitions of a given weight

Call(s)


PART::ListPart(n <,options>)

Parameters

n- any non negative integer

Options

maxlg=l- maximal number of parts of each partition
maxpart=p- outermost possible shape
regular=m- only m-regular partitions are listed
nb- only counts objects

Use the syntax hold(identifier), instead of identifier, if one of the identifiers above is already defined.

Introduction

The PART::ListPart function gives all partitions of n.

A partition of n is a weakly decreasing list of positive integers, called parts, with sum n.

When called with one argument, say n, the function returns the list of all partitions of n.

Given a partition part, _plus(op(part)) gives its weight.

Example 1

>> muEC::PART::ListPart( 4 );
              [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]
>> muEC::PART::ListPart( 5, maxlg=3 );
                [[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1]]
>> muEC::PART::ListPart( 5, maxpart=[3,2], maxlg=3 );
                      [[3, 2], [3, 1, 1], [2, 2, 1]]
>> muEC::PART::ListPart( 100, nb );
                                 190569292

Related Functions

ListPartIn, ListSkewDiag, TYP::IsPart

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MuPAD Combinat, an open source algebraic combinatorics package