Dissecting brick into bars
Combinatorics
2008-09-12 v1
Abstract
An -dimensional parallelepiped will be called a bar if and only if there are no more than different numbers among the lengths of its sides (the definition of bar depends on ). We prove that a parallelepiped can be dissected into finite number of bars iff the lengths of sides of the parallelepiped span a linear space of dimension no more than over . This extends and generalizes a well-known theorem of Max Dehn about partition of rectangles into squares. Several other results about dissections of parallelepipeds are obtained.
Cite
@article{arxiv.0809.1883,
title = {Dissecting brick into bars},
author = {Ivan Feshchenko and Danylo Radchenko and Lev Radzivilovsky and Maksym Tantsiura},
journal= {arXiv preprint arXiv:0809.1883},
year = {2008}
}