Splitting for integer tilings
Izabella {\L}aba, Itay Londner

TL;DR
This paper introduces a new splitting method for analyzing translational integer tilings by finite sets, proving the Coven-Meyerowitz conjecture for new classes of tilings and providing novel combinatorial interpretations and results.
Contribution
The paper presents a new splitting technique and applies it to prove the Coven-Meyerowitz conjecture for specific classes of integer tilings, advancing understanding of tiling structures.
Findings
Proved Coven-Meyerowitz conjecture for tilings with periods involving specific prime factorizations.
Introduced a new combinatorial interpretation of key tools in tiling theory.
Developed a splitting method that simplifies analysis of integer tilings.
Abstract
We consider translational integer tilings by finite sets . We introduce a new method based on \emph{splitting}, together with a new combinatorial interpretation of some of the main tools from our earlier work. We also use splitting to prove the Coven-Meyerowitz conjecture for a new class of tilings . This includes tilings of period with , and tilings of period with , where are distinct primes and . This is the second one of the two papers replacing version 1 of arXiv:2207.11809 (the first one is available as arXiv:2207.11809 v2). The main results of this paper (Theorem 1.2, Corollaries 1.4 and 1.5) and the intermediate results in Section 4.2 are all new and did not appear previously in…
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Taxonomy
Topicsgraph theory and CDMA systems
