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Re: Partition Function


> ... According to the documentation, "NextPartition[p] gives the 
> integer partition following p in reverse lexicographic order."
> 
> Now when I try it, even in a fresh Mathematica session, I get... 
> nothing. Is this a bug or am I just misusing the function? 

Hi.  NextPartition works with a previous partition instead of just a number
like 4.  I really like this package, but I wish there was "better"
documentation on these functions.  Anyway, here's an example:

Needs["DiscreteMath`Combinatorica`"]

Here's a list of partitions:
Partitions[4]
{{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}

NextPartition[{2, 2}]
{2, 1, 1}

It may be easier to just start of with the number in list form:
NextPartition[{4}]
{3, 1}

Looks like NextPartition cycles:
NestList[NextPartition, {4}, NumberOfPartitions[4] + 7]

{{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}, {4}, {3, 1}, 
  {2, 2}, {2, 1, 1}, {1, 1, 1, 1}, {4}, {3, 1}, {2, 2}}

Just another example:
NestList[NextPartition, {4}, NumberOfPartitions[4] - 1]
{{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}

HTH
Dana DeLouis


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