Transformations of 2-port networks and tiling by rectangles
Combinatorics
2022-04-12 v3
Abstract
In this paper, we study 2-port networks and introduce new concepts of voltage drop and -equivalence. The main result is that each planar network is -equivalent to a network with no more than 5 edges. This implies that if an octagon in the shape of the letter can be tiled by squares then it can be tiled by no more than 5 rectangles with rational aspect ratios. Kenyon's theorem from 1998 proves this only for 6 rectangles.
Keywords
Cite
@article{arxiv.2110.02558,
title = {Transformations of 2-port networks and tiling by rectangles},
author = {Svetlana Shirokovskikh},
journal= {arXiv preprint arXiv:2110.02558},
year = {2022}
}
Comments
In English and in Russian. English translation added and minor improvement of exposition performed