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

Jakob Führer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)827-839
Number of pages13
JournalMathematika
Volume68
Issue number3
DOIs
Publication statusPublished - Jul 2022

Keywords

  • Tilings

ASJC Scopus subject areas

  • Mathematics(all)

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