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The Coven–Meyerowitz tiling conditions for 3 odd prime factors

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Main Authors: Izabella, Łaba, Itay, Londner
Format: Book
Language:English
Published: Springer 2023
Subjects:
set A⊂Z tiles
factorization A⊕B=ZM
Online Access:https://link.springer.com/article/10.1007/s00222-022-01169-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7440
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spelling oai:localhost:PNK-74402023-04-03T07:40:54Z The Coven–Meyerowitz tiling conditions for 3 odd prime factors Izabella, Łaba Itay, Londner set A⊂Z tiles factorization A⊕B=ZM CC BY It is well known that if a finite set A⊂Z tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A⊕B=ZM of a finite cyclic group. We are interested in characterizing all finite sets A⊂Z that have this property. Coven and Meyerowitz (J Algebra 212:161–174, 1999) proposed conditions (T1), (T2) that are sufficient for A to tile, and necessary when the cardinality of A has at most two distinct prime factors. They also proved that (T1) holds for all finite tiles, regardless of size. 2023-04-03T07:40:54Z 2023-04-03T07:40:54Z 2022 Book https://link.springer.com/article/10.1007/s00222-022-01169-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/7440 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic set A⊂Z tiles
factorization A⊕B=ZM
spellingShingle set A⊂Z tiles
factorization A⊕B=ZM
Izabella, Łaba
Itay, Londner
The Coven–Meyerowitz tiling conditions for 3 odd prime factors
description CC BY
format Book
author Izabella, Łaba
Itay, Londner
author_facet Izabella, Łaba
Itay, Londner
author_sort Izabella, Łaba
title The Coven–Meyerowitz tiling conditions for 3 odd prime factors
title_short The Coven–Meyerowitz tiling conditions for 3 odd prime factors
title_full The Coven–Meyerowitz tiling conditions for 3 odd prime factors
title_fullStr The Coven–Meyerowitz tiling conditions for 3 odd prime factors
title_full_unstemmed The Coven–Meyerowitz tiling conditions for 3 odd prime factors
title_sort coven–meyerowitz tiling conditions for 3 odd prime factors
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s00222-022-01169-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7440
_version_ 1762184304015704064
score 8.893527

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