On keen Heegaard splittings
  In this paper, we introduce a new concept of {\it strongly keen} for Heegaard splittings, and show that, for any integers $n\geq 2$ and $g\geq 3$, there exists a strongly keen Heegaard splitting of genus $g$ whose Hempel distance is $n$. 
Ayako Ido, Yeonhee Jang, Tsuyoshi Kobayashi
math.GT