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PART::ListPartIn -- list of partitions contained into a given partition or between two given partitions

Call(s)


PART::ListPartIn(part <,partin> <,options>)

Parameters

part, partin- any lists denoting partitions
n- any non negative integer

Options

weight=w- weight of listed partitions is w
nb- only counts objects

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

Introduction

The PART::ListPartIn function gives all partitions contained into the diagram of a given partition. The list is ordered by increasing length.

Called with a second argument Partin, the function returns the list of all partitions contained into the diagram of part and containing the diagram of partin.

Example 1

>> muEC::PART::ListPartIn( [3,1] );
                [[], [1], [2], [3], [1, 1], [2, 1], [3, 1]]
>> muEC::PART::ListPartIn( [3,2,1], [2,1,1] );
               [[2, 1, 1], [2, 2, 1], [3, 1, 1], [3, 2, 1]]
>> muEC::PART::ListPartIn( [4,3,2], weight=6 );
             [[4, 2], [3, 3], [4, 1, 1], [3, 2, 1], [2, 2, 2]]
>> muEC::PART::ListPartIn( [40,30,15,10,8,7,5,3,1], nb );
                                  9631414

Related Functions

ListPart, ListSkewDiag, TYP::IsPart

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MuPAD Combinat, an open source algebraic combinatorics package