Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions

We construct a unilateral lattice tiling of [Formula: see text] into hypercubes of two differnet side lengths p or q. This generalizes the Pythagorean tiling in [Formula: see text]. We also show that this tiling is unique up to symmetries, which proves a variation of a conjecture by Bölcskei from 20...

Descripción completa

Detalles Bibliográficos
Autor principal: Führer, Jakob
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley and Sons Inc. 2022
Materias:
Research Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9358999/
https://www.ncbi.nlm.nih.gov/pubmed/35966410
http://dx.doi.org/10.1112/mtk.12152
Descripción
Sumario:We construct a unilateral lattice tiling of [Formula: see text] into hypercubes of two differnet side lengths p or q. This generalizes the Pythagorean tiling in [Formula: see text]. We also show that this tiling is unique up to symmetries, which proves a variation of a conjecture by Bölcskei from 2001. For positive integers p and q, this tiling also provides a tiling of [Formula: see text].

Ejemplares similares