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Math Help - summa

  1. #1
    Senior Member DivideBy0's Avatar
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    summa

    I've encountered lots of other 'ways' of expressing a sum that are different to

    \sum_{k=1}^n

    Sometimes people put \sum_{cyc}, \sum_{sym}, \sum_{a,b,c}, and sometimes they just put \sum . What does this all mean?? Thanks!
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by DivideBy0 View Post
    I've encountered lots of other 'ways' of expressing a sum that are different to

    \sum_{k=1}^n

    Sometimes people put \sum_{cyc}, \sum_{sym}, \sum_{a,b,c}, and sometimes they just put \sum . What does this all mean?? Thanks!
    I will write for the three variable case:
    cyc means for all "cyclic" permutations
    \sum_{cyc}f(x,y,z) =f(x,y,z)+f(y,z,x)+f(z,x,y)

    I am not sure about this, but I think this means \sum_{sym} means all possible permutations.
    Meaning for three variable case, there will be 6 terms!
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  3. #3
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    Quote Originally Posted by DivideBy0 View Post
    I've encountered lots of other 'ways' of expressing a sum that are different to

    \sum_{k=1}^n

    Sometimes people put \sum_{cyc}, \sum_{sym}, \sum_{a,b,c}, and sometimes they just put \sum . What does this all mean?? Thanks!
    Here is an example. As we want to prove that \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2} for positive numbers.
    We can write,
    \sum_{cyc}\frac{a}{b+c} \geq \frac{3}{2}
    And people take that to mean the entire cyclic sum.
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  4. #4
    Lord of certain Rings
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    Hey DivideBy0,
    Just thought I will add an important point in reading these sums
    Can you tell me what is \sum_{sym}a?
    Consider I have only 3 variables a,b,c...

    Be careful it is a little tricky
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  5. #5
    Senior Member DivideBy0's Avatar
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    Quote Originally Posted by Isomorphism View Post
    Hey DivideBy0,
    Just thought I will add an important point in reading these sums
    Can you tell me what is \sum_{sym}a?
    Consider I have only 3 variables a,b,c...

    Be careful it is a little tricky
    Well... I think that

    \sum_{sym}a=a+b+c ... hope it's right

    Also, there is a section on this in this link.

    It is in 'A less than B' Chapter 2.2

    http://www.mathhelpforum.com/math-he...ss-than-b.html

    Thanks PaulRS for showing me the link, and of course Krizalid and ThePerfectHacker for posting the documents.
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