Lower bounds for the simplexity of the n-cube

TL;DR

This paper establishes a new asymptotic lower bound on the minimum number of simplices needed to dissect an n-dimensional cube, showing it grows at least as fast as (n+1)^{(n-1)/2} without extra vertices.

Contribution

It provides the first asymptotic lower bound for the simplexity of n-cubes in simplicial dissections without additional vertices.

Findings

Lower bound of (n+1)^{(n-1)/2} simplices for dissections

Asymptotic growth rate of simplexity established

Improves understanding of cube dissection complexity

Abstract

In this paper we prove a new asymptotic lower bound for the minimal number of simplices in simplicial dissections of $n$-dimensional cubes. In particular we show that the number of simplices in dissections of $n$-cubes without additional vertices is at least $(n+1)^{\frac {n-1} 2}$.