Re: sum over i+j+k==n
- To: mathgroup at smc.vnet.net
- Subject: [mg84447] Re: sum over i+j+k==n
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Mon, 24 Dec 2007 04:52:11 -0500 (EST)
- References: <fkla8k$3v1$1@smc.vnet.net>
Jack Kennedy wrote:
> Hi All,
> I often find myself needing to sum over triples
> (or other tuples) like i,j,k where i+j+k=n. Is there
> a convenient way to write this in Mathematica?
You didn't mention exactly how do you wish to write n as a sum of three
numbers. In Mathematica 6, the Combinatorica package has
IntegerPartitions[], which does it one way. For example:
In[1]:= << Combinatorica`
In[2]:= IntegerPartitions[10, {3}]
Out[2]= {{8, 1, 1}, {7, 2, 1}, {6, 3, 1}, {6, 2, 2}, {5, 4, 1}, {5, 3,
2}, {4, 4, 2}, {4, 3, 3}}
(IIRC in earlier versions Combinatorica could be loaded with
<<DiscreteMath`Combinatorica`)
I hope this helps,
Szabolcs