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Dec
31
reviewed Approve To determine Nullity of $T$
Dec
31
comment A generalized derivative
@user62029 I have a copy of this one. Take a look at it.
Dec
31
accepted Does the maximum cut implies the minimum flow?
Dec
31
accepted How do we define interior and exterior of a geometric figure?
Dec
31
accepted How to solve this kind of problem?
Dec
31
accepted How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$?
Dec
31
comment How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$?
Hey, I've finally been able to understand it. I've posted it as an answer below.
Dec
31
answered How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$?
Dec
28
asked How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$?
Dec
27
accepted What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$?
Dec
27
comment What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$?
But anything that is expressed with one could also be expressed with the other, right? Disregarding if they have good closed expressions.
Dec
27
comment How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$?
I just need to do that? There's nothing that could be made with that definition so that it would result in ${-1 \choose 0}=1$?
Dec
27
asked How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$?
Dec
27
accepted How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that $ {-n \choose -n}=0$?
Dec
27
comment How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that $ {-n \choose -n}=0$?
Yes. Thanks. I thought it would make some kind of sense to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ alone. I am having lectures on introductory combinatorics and my professor told us that $k,x$ only make sense when non-negative integers with $k\geq x$, then I started reading Knuth/Patashnik/Graham's Concrete Mathematics and there he uses almost arbitrary $k,x$'s. I'm on an exploratory work on this new concepts.
Dec
27
asked How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that $ {-n \choose -n}=0$?
Dec
27
accepted Why $ {-1\choose 3}=-1$?
Dec
27
accepted What is the convolution here?
Dec
27
comment Why $ {-1\choose 3}=-1$?
That's it. It makes more sense to see $\alpha - (k-1)$. This way, it seems that $(k-1)$ is entirely on the plot. Seeing $a-k+1$ is like $k$ was the protagonist and $1$ have nothing to do with it.
Dec
27
comment Why $ {-1\choose 3}=-1$?
I don't get it. So instead of reaching $k$, I should reach $k-1$?