Bárány, Imre;
Frankl, Péter;
(2023)
Cells in the box and a hyperplane.
Journal of the European Mathematical Society
, 25
(7)
pp. 2863-2877.
10.4171/JEMS/1252.
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Abstract
It is well known that a line can intersect at most 2n−1 cells of the n×n chessboard. Here we consider the high dimensional version: how many cells of the d-dimensional n × . . . × n box can a hyperplane intersect? We also prove the lattice analogue of the following well-known fact. If K, L are convex bodies in R d and K ⊂ L, then the surface area of K is smaller than that of L.
| Type: | Article |
|---|---|
| Title: | Cells in the box and a hyperplane |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/JEMS/1252 |
| Publisher version: | http://dx.doi.org/10.4171/jems/1252 |
| Language: | English |
| Additional information: | Copyright © 2022 European Mathematical Society. Published by EMS Press and licensed under a CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Lattices, polytopes, lattice points in convex bodies |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10188056 |
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