MathOverflow

The Dean Conjecture (proven by Fisher, and later by Havet and Thomassé in 2000) states that every tournament contains at least one vertex $v$ such that $|N^{++}(v)| \geq |N^{+}(v)|$.
The Havet and Thomassé proof was very important for the use of Median Orders in tournament theory. This led to an increase in attempts to use similar ordering techniques for the broader Seymour Second Neighborhood Conjecture (SSNC). This result itself...

Consider the Cantor set $\mathcal C$. It's pretty fundamental! Part of the reason it's fundamental is that it shows up in many different guises all across mathematics. For example:
There are analytic variants (alternative subsets of $[0,1]$) which are homeomorphic to $\mathcal C$ but which can have radically different analytic properties....

Can anybody provide references of semilinear equations in $\mathbb{R}^N$ which involve operator like $(-\Delta)^s\pm (-\Delta)$ with $0<s<1.$ Does this equation arise in physics or any application based phenomena. Please note, I am not looking...

I am currently trying to work with the Cohen forcing $\mathrm{Add}(\kappa, \lambda^+)$ with $\kappa$ infinite and regular and $\lambda> \kappa$. In my setting I want to preserve some large cardinal property of $\lambda$ in the generic extension and...