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comment Gaussian proof for the sum of squares?
Spectacular! Thanks for posting it.
Aug
21
awarded  Popular Question
Aug
17
comment What's the name of $\sum_{k = 0}^{n} (-1)^k {n \choose k} (n-k)^w$?
@PedroTamaroff: thanks! Your comment pointed me in the right direction. According the the Wikipedia page on the I-E principle, the expression I found equals $n! \, S(w, n)$, where $S(w, n)$ is a "Stirling number of the second kind"...
Aug
17
asked What's the name of $\sum_{k = 0}^{n} (-1)^k {n \choose k} (n-k)^w$?
Jul
23
awarded  Yearling
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2
awarded  Curious
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2
awarded  Inquisitive
May
17
awarded  Nice Question
Apr
12
revised Looking for a a measure-theoretic treatment of “differential entropy”
added 140 characters in body
Apr
10
asked What's the name of the quantity $\mathbb{P}(A\cap B)/(\mathbb{P}(A)\mathbb{P}(B))\;$?
Apr
10
asked Looking for a a measure-theoretic treatment of “differential entropy”
Apr
7
awarded  Nice Question
Apr
7
accepted How to recognize adjointness?
Apr
6
asked How to recognize adjointness?
Apr
5
accepted What are integrating factors, really?
Apr
5
awarded  Civic Duty
Apr
5
asked What are integrating factors, really?
Mar
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awarded  Notable Question
Mar
17
comment Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
@Sabyasachi: sorry, I had not finished with my comment. Also, on the contrary, I think your proof is extremely elegant. I'm making the case for inelegance here.
Mar
17
comment Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
$\dots\;\;$ These means that $\nset$ can be partitioned according to the $d$ factor of these products, and the size of each partition is $\varphi(n/d)$. But don't get me wrong: such proofs are OK, as quick ways to convince oneself that something is true, but one needs to go beyond them to get at the essence of why something is true.