Hi all. Today in my research I found a conjecture.
Let $S$ be the set of all words of a language. Define the function $N: S\times S \rightarrow R_+$ such that $N(x, y) = $ number of journal articles about $x$ that the word $y$ appears. Obviously: $N(x, x) \ge N(x, y)$ for all $x, y \in S$ and it can be assumed that the $N(x,x) = N(x,y)$ only for $x=y$.
Define $dep(x, y) = N(x, x) - N(x,y)$. Is $dep$ a quasimetric?