## Re: [PrimeNumbers] Digest Number 2050

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• ... I had not heard the name multisets before. I can use that terminology in the future. multisets if multiplicities are allowed, and sets if multiplicities
Message 1 of 1 , Dec 17, 2006
"Phil Carmody" thefatphil@... thefatphil wrote:

> These aren't sets, they're multisets.
>
I had not heard the name "multisets" before.
I can use that terminology in the future.
multisets if multiplicities are allowed,
and sets if multiplicities are not allowed.

>>
>>
>>
>
> This does not define a Matrix Addition table.
>

THE name I chose confused the issue. It's not an addition table for
matrices.
It's a matrix which is also an addition table.
> Is
> 0 0
> 0 0
> such a table?
>
>
Yes. Because, 0 + 0 = 0.

> Is
> 1 4
> 9 16
> such a table?
>
>
No, because 16 is not 4 + 9.

>> What would you estimate, for general preset Matrix Factor Element Sets,
>> the complexity of this problem to be?
>>
>
> Given that you've not defined your terms, it's impossible.
>
>
I tried.
Perhaps if we discuss it more, we can work through all the confusions.

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>
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>
>
> _______________________________________________________________
>
> 2b. Re: Another example of Matrix Factor Elements and Addition table
> Posted by: "Phil Carmody" thefatphil@... thefatphil
> Date: Sun Dec 17, 2006 1:58 am ((PST))
>
> --- Kermit Rose <kermit@...> wrote:
>
>> The fundamental Matrix Factor Elements are;
>> [0, 3, 6, 9, 14, 16, 17, 18, 19]
>>
>>
>> 0 2 4 6 8 10 11
>> 2 4 6 8 10 12 13
>> 5 7 9 11 13 15 16
>> 8 10 12 14 16 18 19
>>
>
> So it's a set { a_{i,j} : a_{i,j} = a_{1,j} + a_{i,1} if i>1 or j>1 }
>
> In that case, the whole thing becomes trivial.
>
> Sum { 2^{a_{i,1}} } * Sum { 2^{a_{1,j}} } = N
>
> So if N is prime, no such representation exists.
>
> Phil
>
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> __________________________________________________
>

Exactly so! The proof for the theorem is quite trivial.

But I hope that the theorem itself is quite profound.

Kermit < kermit@... >
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