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>>6613067 Considering I don't know much about the requirements for the actual problem you can just post the answer if you want. I'd probably get more learning out of studying the solution.

>>6613099 Well, i'll read it through later if i have time. Altough i think the multinomial coefficient can be further generalized into matrices of sums. Usually the generalizations of these types end in that "type of level of abstraction", look at the proof for the matrix representation of the statistical version of "least square" approximation. I can feel that the end term on the right side at the end can be further generalized, its not powerful enough. Sorry.

Perphaps you need to introduce some new definitions or something.

>>6613135 It's actually really easy to understand even if you have very little math experience.

Let's say you wanted to find the coefficient of some term in the expansion of (x1)(x1+x2)(x1+x2+x3)(x1+x2+x3+x4)...(x1+...+xm)

You could do FOIL, which means m! multiplications, and then add up all the like terms until you get the coefficient you want. But that's sort of a pain in the ass.

Or you can generate the coefficient using the formula I came up with.

Let's say m=6 and the term you want to look at is (x1)^3(x2)^2(x3)^1. Well the coefficient is (3*4*4*3*2*1)/(3!2!1!0!0!0!) = 24

>>6613046 I think it's great to find out these kind of things on your own. But I don't think this is novel and powerful enough to publish. I mean i have taken undergrad courses where we used techniques that came pretty close, so i can;t imagine this is now known.

Perhaps my advise to do some research into what is already known and see how this could possibly relate to existing research.

>>6613181 Well I don't really see how to further organize the part I posted. Perhaps multiindex notation could be used but I don't think it's particularly helpful here.

>>6613193 I have searched this extensively and I can't find anything like it. There really is not a lot of work on generalizing the Multinomial Theorem and what is there is mostly about continuous powers.

>>6613205 perhaps you should make it into a complete "nomial" thing. With an introduction to the simple binomial coefficient, and then build yourself up slowly to your generalization?

My advice is to find a math professor (preferably a friend of a friend) who is knowledgeable in this area. Then have them go over it as an unofficial review. They will be able to give you excellent advice as to what you should or shouldn't be doing.

Unfortunately, there's more to publishing than just the content of the manuscript. The reviewers need to know where you're coming from and what you think you're doing and where your work stands in the literature. By referencing the relevant, current literature, you will inevitably ingratiate yourself to people quite likely to review you. That, for better or worse, is how it works.

>>6613170 I'm an engineer and I can integrate that, but why should I when I can just find the area with triangles?

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