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Re: rules on vector sequence

• To: mathgroup at smc.vnet.net
• Subject: [mg98080] Re: [mg98018] rules on vector sequence
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sun, 29 Mar 2009 02:48:24 -0500 (EST)
• References: <200903281041.FAA04380@smc.vnet.net>
• Reply-to: drmajorbob at bigfoot.com

Here's a solution:

Clear[sums, insertions]
insertions[x : {__List}] := Union @@ insertions /@ x
insertions[x_List] := Union[Insert[x, 0, #] & /@ Range[1 + Length@x]]
sums[1] = {};
sums[2] = {{-2, 2}, {-1, 1}, {1, -1}, {2, -2}};
sums[4] = Module[{nonZero = {-2, -1, 1, 2}},
    Union @@
     Permutations /@
      Join[Select[Tuples@{nonZero, nonZero, nonZero, nonZero},
        0 == Total@# &], insertions@insertions@sums@2]
    ];
sums[len_?Positive] := sums[len] = insertions@sums[len - 1]

Timing[Length@sums@17]

{7.9271, 86224}

sums@3

{{-2, 0, 2}, {-2, 2, 0}, {-1, 0, 1}, {-1, 1, 0}, {0, -2, 2}, {0, -1,
   1}, {0, 1, -1}, {0, 2, -2}, {1, -1, 0}, {1, 0, -1}, {2, -2, 0}, {2,
   0, -2}}

Length@sums@4

60

Length@sums@5

220

s6 = sums@6;
Length@s6
Total /@ s6 // Union
Total /@ Unitize@s6 // Union
Length@s6 == Length@Union@s6

600

{0}

{2, 4}

True

Bobby


On Sat, 28 Mar 2009 05:41:26 -0500, Filippo Miatto  
<sottosupremo 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..
> thank you in advance!
> Filippo
>



-- 
DrMajorBob at bigfoot.com

• References:
  • rules on vector sequence
    • From: Filippo Miatto <sottosupremo@gmail.com>