Maximal volumes of pyramids in the unit cube

Abstract

Let $Q_n=[0,1{]}^n$, $n\ge 2$. Denote by $M_n$ be the maximal volume of a pyramid in $Q_n$ whose base is a hyperplane section of $Q_n$, and by $M_n^0$ the corresponding maximum when the section contains the center of $Q_n$. We prove that $n{M}_n<(n+1)M_{n+1}^0$.