Re: Partition Function

• To: mathgroup at smc.vnet.net
• Subject: [mg57662] Re: Partition Function
• From: "Dana DeLouis" <delouis at bellsouth.net>
• Date: Fri, 3 Jun 2005 05:33:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> ... 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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