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Re: [PrimeNumbers] Digest Number 2050

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  • Kermit Rose
    ... 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
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      "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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      >
      > _______________________________________________________________
      >
      > 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]
      >>
      >> The addition table is:
      >>
      >> 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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