Grigory M
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 Jan16 reviewed Reject If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ Prove that $\det(AD)=\det(BC)$ Jan15 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. Jan15 reviewed Close If $f$ is an injection, $f(S_1 \cap S_2) = f(S_1) \cap f(S_2)$ Jan15 reviewed Close Every continuous function $f:[0,1]\rightarrow \mathbb{R}$ is bounded above Jan15 reviewed Close Simplify the following fraction $\frac {2+3i}{6-i}$ Jan15 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ @655321 though there is one example that is explained in detail in many books (e.g. in Enumerative Combinatorics): Lagrange inversion formula Jan15 comment Finite summation with binomial coefficients, $\sum (-1)^k\binom{r}{k} \binom{k/2}{q}$ @655321 I'm afraid I don't know a good reference... Jan15 reviewed Close Set Theory intersection and union Jan15 reviewed Looks OK Online tool for making graphs (vertices and edges)? Jan14 reviewed Approve Set theory questions about $ϵ$ and concatenation Jan14 reviewed No Action Needed Decomposition if matrix with strongly correlated columns Jan14 reviewed Leave Closed Integral $\int \frac{dx}{\left(1+x^{2014}\right)\left(1+x^{\alpha}\right)},\quad \alpha\neq 0.$ Jan14 reviewed Reject Euler path in cube Jan14 comment Embedding of two-dimensional CW complexes which induces a zero homomorphism on second homotopy groups x-posted to MO: mathoverflow.net/q/193845 Jan14 comment When $\frac{C(n, k)}{n^{k-1}} > 1$? Well, for $n=k!+t$ we need to compare $(1+t/k!)\cdot(1-1/(k!+t))(1-2/(k!+t))\ldots(1-(k-1)/(k!+t))$ withs 1. Shouldn't be hard (take logarithm, bound it...) — and at least genesis of $s_k$ is clear. Jan13 reviewed Close Show that the function $d(x, y)$ is a metric on the set $\mathbb R^2$ . Jan13 reviewed No Action Needed Baby Rudin: Chapter 1, Problem 6{d}. How to complete this proof? Jan13 reviewed Close Prove Summation to Some Number $n$ Jan13 reviewed Approve How to calculate $\lim \limits_{x \to 0}{\frac{\sqrt{1 + x + x^2} - 1}{x}}$? Jan13 reviewed Close $\lim_{n \to \infty}\sqrt{2+\sqrt{2+\sqrt{2}+\sqrt{2}}}$