Naslov
Torus Square tilings

Autori
Dutour Sikirić, Mathieu

Izvornik
Applicable algebra in engineering communication and computing (0938-1279) 23 (2012), 5/6; 251-261

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Square tilings; harmonic vectors; electrical networks

Sažetak
We consider periodic square tilings of the plane. By extending a formalism introduced in 1940 for tiling of rectangles by squares we build a correspondence between periodic plane maps endowed with a periodic harmonic vector and periodic square tilings satisfying a regularity condition. The space of harmonic vectors is isomorphic to the first homology group of a torus. So, periodic plane square tilings are described by two parameters and the set of parameters is split into angular sectors. The correspondence between symmetry of the square tiling and symmetry of the corresponding plane map and harmonic vector is discussed and a method for enumerating the regular periodic plane square tilings having r orbits of squares is outlined.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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