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

Jakob Führer

doi:10.1112/mtk.12152

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

Jakob Führer^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a unilateral lattice tiling of (Formula presented.) into hypercubes of two differnet side lengths p or q. This generalizes the Pythagorean tiling in (Formula presented.). 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 presented.).

Original language	English
Pages (from-to)	827-839
Number of pages	13
Journal	Mathematika
Volume	68
Issue number	3
DOIs	https://doi.org/10.1112/mtk.12152
Publication status	Published - Jul 2022

Keywords

Tilings

ASJC Scopus subject areas

Mathematics(all)

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10.1112/mtk.12152Licence: CC BY 4.0

Cite this

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abstract = "We construct a unilateral lattice tiling of (Formula presented.) into hypercubes of two differnet side lengths p or q. This generalizes the Pythagorean tiling in (Formula presented.). We also show that this tiling is unique up to symmetries, which proves a variation of a conjecture by B{\"o}lcskei from 2001. For positive integers p and q, this tiling also provides a tiling of (Formula presented.).",

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

Abstract

Keywords

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