{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:44Z","timestamp":1753893824623,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Keller's conjecture on cube tilings asserted that, in any tiling of $\\mathbb{R}^d$ by unit cubes, there must exist two cubes that share a $(d-1)$-dimensional face. This is now known to be true in dimensions $d\\leq 7$ and false for $d\\geq 8$. In this article, we propose analogues of Keller's face-sharing property for integer tilings. We construct counterexamples to a ``strong\" version of this property, and prove that a weaker version holds for integer tilings under appropriate additional assumptions.<\/jats:p>","DOI":"10.37236\/13002","type":"journal-article","created":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T12:32:50Z","timestamp":1732797170000},"source":"Crossref","is-referenced-by-count":2,"title":["Keller Properties for Integer Tilings"],"prefix":"10.37236","volume":"31","author":[{"given":"Benjamin","family":"Bruce","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Izabella","family":"\u0141aba","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,11,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T12:32:50Z","timestamp":1732797170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,29]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/13002","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,11,29]]},"article-number":"P4.47"}}