Re: rules on vector sequence

• To: mathgroup at smc.vnet.net
• Subject: [mg98089] Re: rules on vector sequence
• From: Raffy <raffy at mac.com>
• Date: Sun, 29 Mar 2009 03:22:57 -0500 (EST)
• References: <gqkurj\$47q\$1@smc.vnet.net>

```On Mar 28, 3:40 am, Filippo Miatto <sottosupr... at gmail.com> wrote:
> Dear all,
> I need to generate all the vectors, of a given length N, that have
> these three properties:
>
> 1- the entries have to be among -2,-1,0,1,2
> 2- the sum of all the entries has to be 0
> 3- only two or four of the entries can be different from 0
>
> do you have any suggestions on how i can do that? i tried something
> but without success.. expecially i don't know how to implement the
> third rule..
> Filippo

filippo[n_Integer, nz_Integer] :=
Join @@ (Permutations[PadRight[#, n]] & /@
Select[Tuples[{-2, -1, 0, 1, 2}, nz], Total[#] == 0 &]);

n : length of vector
nz : number of entries not explicitly set to 0

filippo[4, 2] ==> {{-2,2,0,0},{-2,0,2,0},{-2,0,0,2},{2,-2,0,0},
{2,0,-2,0},{2,0,0,-2},{0,-2,2,0},{0,-2,0,2},{0,2,-2,0},{0,2,0,-2},
{0,0,-2,2},{0,0,2,-2},{-1,1,0,0},{-1,0,1,0},{-1,0,0,1},{1,-1,0,0},
{1,0,-1,0},{1,0,0,-1},{0,-1,1,0},{0,-1,0,1},{0,1,-1,0},{0,1,0,-1},
{0,0,-1,1},{0,0,1,-1},{0,0,0,0},{1,-1,0,0},{1,0,-1,0},{1,0,0,-1},
{-1,1,0,0},{-1,0,1,0},{-1,0,0,1},{0,1,-1,0},{0,1,0,-1},{0,-1,1,0},
{0,-1,0,1},{0,0,1,-1},{0,0,-1,1},{2,-2,0,0},{2,0,-2,0},{2,0,0,-2},
{-2,2,0,0},{-2,0,2,0},{-2,0,0,2},{0,2,-2,0},{0,2,0,-2},{0,-2,2,0},
{0,-2,0,2},{0,0,2,-2},{0,0,-2,2}}

```

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