MathOverflow

Let $x_0,x_1,...x_n,y_0,y_1,...,y_n$ be nonnegative real numbers and $z_0,z_1,...,z_{2n}$ satisfy $z_k=\sum_{i+j=k}x_iy_j$. Define $$F(x_0,x_1,...,x_n)=\left(\sum_{k=0}^nx_k\right)\left(\sum_{k=0}^nx_k^3\right)-\left(\sum_{k=0}^nx_k^2\right)^2=\sum_...

Is there an example of a finite family $\mathcal{F}$ of finite sets, size of the family $n$, and with the property that every union of $\lfloor (n+1)/2 \rfloor$ sets in $\mathcal{F}$ belongs to $\mathcal{F}$, in which there is no element in at least...

Let $ABC$ be a triangle with $H$, $O$ be the its orthocenter and the circumcenter respectively. If the three triangles $A^\prime BC$, $AB^\prime C$ and $ABC^\prime$, constructed on the sides of a triangle $ABC$ as bases, are similar, isosceles and similarly...

A continuous map $f: X\to Y$ gives naturally a notion of pullback $f^*$ in cohomology. A map between cohomology groups $H^n(X;G) \to H^m(X;A)$ that commutes with $f^*$ is a cohomology operation of type $(n,m,G,A)$ (where $G$ and $A$ are Abelian groups...