Back to Search
Start Over
Transformations of 2-port networks and tiling by rectangles
- Publication Year :
- 2021
-
Abstract
- In this paper, we study 2-port networks and introduce new concepts of voltage drop and $\Pi$-equivalence. The main result is that each planar network is $\Pi$-equivalent to a network with no more than 5 edges. This implies that if an octagon in the shape of the letter $\Pi$ 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.<br />Comment: In English and in Russian. English translation added and minor improvement of exposition performed
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Language :
- English
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.02558
- Document Type :
- Working Paper