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Jan
17
comment Showing ${n + a - 1 \choose a - 1} = \sum_{k = 0}^{\left\lfloor n/2 \right\rfloor} {a \choose n-2k}{k+a-1 \choose a-1}$
cf. math.stackexchange.com/q/601940 etc
Jan
17
comment Elementary proof of the fact that any orientable 3-manifold is parallelizable
«The second surprise in this story» — that's, IMHO, the most interesting part...
Jan
17
comment Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$
@1234 $\frac{P(x)+P(-x)}2$ extracts even terms from any polynomial $P$, you know...
Jan
17
comment Closed-form solution for $f(n) = \sum_{k>0}\binom{n}{2k}x^{k}$ without $\sqrt{x}$
Well, do you know the answer for just $\sum \binom nlx^l$?
Jan
17
comment Elementary proof of the fact that any orientable 3-manifold is parallelizable
Do you know the standard proof («$w_1=w_2=0$ implies parallelizable by elementary obstruction theory» + «$w_1=0$ implies $w_2=0$ by Wu's formulas»)? It's not that hard — and at least the first part is, in a sense, the most straightforward approach possible (but I indeed don't know any intuitive explanation of the second part).
Jan
16
reviewed Leave Closed $\mathcal A$ is empty, what is $\bigcap_{S\in\mathcal A}S$?
Jan
16
comment If $a,b,c$ are real numbers all less than or equal to $1$ such that $a+b+c=0$ , then is it true that $(1-a)(1-b)(1-c) \le 1$?
«which is true» — why, actually? ($ab$ can be negative)
Jan
16
comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$?
OK, I apologise — this question was not completely clear as written — but it's a) not a duplicate of the linked question; b) can be reasonably answered.
Jan
16
comment On ${-1 \choose 0}=1$, can I assume that $\frac{(-1)!}{(-1)!}=1$?
related: 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 ${-1\choose 0}=1$?
Jan
16
reviewed Looks OK Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
Jan
16
reviewed Leave Open Intersecting Circumcircles
Jan
16
reviewed Leave Closed Finding the closed form for $\sum_{n=1}^{\infty }\frac{\zeta (4n)}{\beta^{4n-1}}$
Jan
16
reviewed Looks OK constant-curvature Riemannian metric for Bring's surface
Jan
16
reviewed Looks OK Proof that $f:\mathbb R\to[-1,1], f(x)=\cos x$ is surjective
Jan
16
reviewed No Action Needed The convergence of $ \sum_{n=2}^{+\infty} \frac{1}{\sqrt{n}} \ln(\frac{n+1}{n-1})$
Jan
16
reviewed No Action Needed conjugation of Lie groups and homotopy group
Jan
16
reviewed Reject If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ Prove that $\det(AD)=\det(BC)$
Jan
15
comment Unimodality of q-binomial coefficients
Unimodality of q-binomial coefficients is a difficult theorem, proved more than 20 years after it was conjectured. If you're really interested in a proof — it's easy to google references.
Jan
15
reviewed Close If $f$ is an injection, $f(S_1 \cap S_2) = f(S_1) \cap f(S_2)$
Jan
15
reviewed Close Every continuous function $f:[0,1]\rightarrow \mathbb{R}$ is bounded above