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#1 2007-10-02 09:04:16
- Ricky
- Moderator
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Linearly algebraic combinatorics...
...and yes, I made that name up (or so I think). Anyways, here is the problem:
S is finite set of polynomials generated by unknowns x and y. For any positive integer n, Omega_n(S) is the collection of all polynomials formed by multiplying elements of S at most n times. For example, if S = {x, y}, then Omega_2(S) = {x, y, x^2, xy, y^2}. Also, let d_n(S) be the number of linear independent polynomials.
Find the least upper bound over all such sets of:
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
#2 2007-10-25 05:41:43
- bossk171
- Power Member
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Re: Linearly algebraic combinatorics...
Woah, cool. Care to explain what the answer is? I have the feeling it'll be a bit over my head...
Most of that made sense to me (I had to read through it a few times) but what does that line over the limit mean? That's the first time I've seen that.
(Just a comprehension check. Omega_3(S) = {x, y, x², y², x³, y³, xy, x²y, xy²})
There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.