Normal-sized hypercuboids in a given hypercube
Combinatorics
2025-01-03 v4 Number Theory
Abstract
In a given hypercube, draw grid lines parallel to the edges, and consider all hypercuboids (or hypercubes) whose edges are lying on the grid lines or the boundary. We find the limit of the value of the ratio of the arithmetic mean of the volumes of those hypercuboids (or hypercubes) to the entire volume as the grid spacing becomes smaller.
Cite
@article{arxiv.2211.15342,
title = {Normal-sized hypercuboids in a given hypercube},
author = {Takashi Hirotsu},
journal= {arXiv preprint arXiv:2211.15342},
year = {2025}
}
Comments
3 pages