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Help! How to calculate additive partitions?

• To: mathgroup at smc.vnet.net
• Subject: [mg34432] Help! How to calculate additive partitions?
• From: "Thomas Brodhead" <Tom.Brodhead at worldnet.att.net>
• Date: Sun, 19 May 2002 04:15:06 -0400 (EDT)
• Organization: AT&T Worldnet
• Sender: owner-wri-mathgroup at wolfram.com

Help!

I need to find a formula or method that will allow me to calculate the
additive partitions of a given number.

E.g., 3 can be expressed as

1+1+1
2+1
1+2
3

IMPORTANT: Even though 2+1 and 1+2 employ the same values, the order is
important and thus the procedure or formula that I need would need to
produce both of those results.

Likewise, 4 would break down this way:
1+1+1+1
2+1+1
1+2+1
1+1+2
2+2
3+1
1+3
4

I need to calculate both the number of results that I should get, and the
results themselves.

How can this be done?

Many thanks,
--Tom
---------------------------------------------------------
Tom Brodhead
http://home.att.net/~tom.brodhead/
---------------------------------------------------------

• Follow-Ups:
  • Re: Help! How to calculate additive partitions?
    • From: "Fred Simons" <f.h.simons@tue.nl>
  • Re: Help! How to calculate additive partitions?
    • From: Murray Eisenberg <murraye@attbi.com>