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...

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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
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author Führer, Jakob
author_facet Führer, Jakob
author_sort Führer, Jakob
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description 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].
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spelling pubmed-93589992022-08-10 Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions Führer, Jakob Mathematika Research Articles 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]. John Wiley and Sons Inc. 2022-06-07 2022-07 /pmc/articles/PMC9358999/ /pubmed/35966410 http://dx.doi.org/10.1112/mtk.12152 Text en © 2022 The Authors. Mathematika is copyright © University College London and published by the London Mathematical Society on behalf of University College London. https://creativecommons.org/licenses/by/4.0/This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Articles
Führer, Jakob
Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title_full Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title_fullStr Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title_full_unstemmed Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title_short Filling space with hypercubes of two sizes – The pythagorean tiling in higher dimensions
title_sort filling space with hypercubes of two sizes – the pythagorean tiling in higher dimensions
topic Research Articles
url 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
work_keys_str_mv AT fuhrerjakob fillingspacewithhypercubesoftwosizesthepythagoreantilinginhigherdimensions

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