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arXiv · 2110.02558

Transformations of 2-port networks and tiling by rectangles

Svetlana Shirokovskikh
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Abstract

In this paper, we study 2-port networks and introduce new concepts of voltage drop and $Π$-equivalence. The main result is that each planar network is $Π$-equivalent to a network with no more than 5 edges. This implies that if an octagon in the shape of the letter $Π$ 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.

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Svetlana Shirokovskikh. 2022-04-09. Transformations of 2-port networks and tiling by rectangles. https://arxiv.org/abs/2110.02558

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