Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: simple set operations
  • Next by Date: Re: simple set operations
  • Previous by thread: Re: Partition Function
  • Next by thread: Re: PostScipt from Mathlink