{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:17:15Z","timestamp":1772515035400,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $A$ be a finite multiset of integers. A second multiset of integers $T$ is said to be an $A$-tiling of level $d$ if every integer can be expressed in exactly $d$ ways as the sum of an element of $A$ and of an element of $T$. The set $T$ is indecomposable if it cannot be written as the disjoint union of two proper subsets that are also $A$-tilings. In this paper we show how to construct indecomposable tilings that have exponentially long periods. More precisely, we give a sequence of multisets $(A_k)_{k=1}^{\\infty}$ such that each $A_k$ admits an indecomposable tiling $T_k$ of period greater than $e^{c\\root 3\\of{n_k\\log(n_k)}}$ where $n_k = {\\rm diam}(A_k) = \\max\\{j \\in A_k\\} - \\min\\{j \\in A_k\\}$ tends to infinity and where $c &gt; 0$ is some constant independent of $k$.<\/jats:p>","DOI":"10.37236\/1933","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:09Z","timestamp":1578719469000},"source":"Crossref","is-referenced-by-count":3,"title":["Indecomposable Tilings of the Integers with Exponentially Long Periods"],"prefix":"10.37236","volume":"12","author":[{"given":"John P.","family":"Steinberger","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,7,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:48:06Z","timestamp":1579322886000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1933","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,7,29]]},"article-number":"R36"}}