# Terlaky, Tamas

## Continous analogue of Hirsch conjecture ★★

Author(s): Deza; Terlaky; Zinchenko

\begin{conjecture} The order of the largest total curvature of the primal central path over all polytopes defined by $n$ inequalities in dimension $d$ is $n$. \end{conjecture}

Keywords: curvature; polytope

## Average diameter of a bounded cell of a simple arrangement ★★

Author(s): Deza; Terlaky; Zinchenko

\begin{conjecture} The average diameter of a bounded cell of a simple arrangement defined by $n$ hyperplanes in dimension $d$ is not greater than $d$. \end{conjecture}

Keywords: arrangement; diameter; polytope