#Is it true identity?

13 messages · Page 1 of 1 (latest)

round ermine
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I've seen it somewhere on math classes but dunno if it's correct and how to prove it. It works for small examples, bi and n are natural, and ai are some positive real
And if it is actually true how do we call it?

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pale tapirBOT
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feral wind
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this is soo new to me

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is it binomial theorem no its not

tender hill
jade flintBOT
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dark matter

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cerulean forge
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Reminds me, by considering, for integers $i_1,…,i_r$, such that their sum is $n$ the set $\mathscr{D}(i_1,…,i_r,n)$ which is the set of partitions $(I_j)_{1 \le j \le r}$ such that $|I_j|=i_j$ for all j in ${1,…,r}$ you can prove that $|\mathscr{D}(i_1,…,i_r,n)|=\frac{n!}{i_1!….i_r!}$

jade flintBOT
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😑 ɿototoЯ | Rototor 😑

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cerulean forge
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There is a nice proof using the natural group action of S_n on that set (that is transitive), calculating the cardinal of the stabiliser of one of the elements of the set and using the orbit stabiliser theorem

rotund novaBOT
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@round ermine

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round ermine
#

+close

rotund novaBOT
# round ermine +close
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