Cells in the box and a hyperplane
Imre Bárány
Renyi Institute of Mathematics, Budapest, Hungary; University College London, UKPéter Frankl
Renyi Institute of Mathematics, Budapest, Hungary
![Cells in the box and a hyperplane cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-25-issue-7.png&w=3840&q=90)
Abstract
It is well known that a line can intersect at most cells of the chessboard. Here we consider the high-dimensional version: how many cells of the -dimensional box can a hyperplane intersect? We also prove the lattice analogue of the following well-known fact: if are convex bodies in and , then the surface area of is smaller than that of .
Cite this article
Imre Bárány, Péter Frankl, Cells in the box and a hyperplane. J. Eur. Math. Soc. 25 (2023), no. 7, pp. 2863–2877
DOI 10.4171/JEMS/1252