{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T23:27:33Z","timestamp":1703028453725},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> A cross in Rn is a cluster of unit cubes comprising a central one and 2n arms. In their monograph Algebra and Tiling, Stein and Szab\u00f3 suggested that tilings of \u211d<jats:sup>n<\/jats:sup> by crosses should be studied. The question of the existence of such a tiling has been answered by various authors for many special cases. In this paper we completely solve the problem for \u211d<jats:sup>2<\/jats:sup>. In fact we do not only characterize crosses for which there exists a tiling of \u211d<jats:sup>2<\/jats:sup> but for each cross we determine its maximum packing density.<\/jats:p>","DOI":"10.1515\/ms-2015-0063","type":"journal-article","created":{"date-parts":[[2015,12,11]],"date-time":"2015-12-11T05:47:39Z","timestamp":1449812859000},"page":"935-956","source":"Crossref","is-referenced-by-count":2,"title":["Packing of \u211d<sup>2<\/sup> by Crosses"],"prefix":"10.1515","volume":"65","author":[{"given":"C. N.","family":"Cruz","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, PORTUGAL"}]},{"given":"A. M.","family":"d\u2019Azevedo Breda","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, PORTUGAL"}]},{"given":"M. R.","family":"Pinto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, PORTUGAL"}]}],"member":"374","published-online":{"date-parts":[[2015,12,9]]},"container-title":["Mathematica Slovaca"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0063\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0063\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T07:11:42Z","timestamp":1624345902000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/ms-2015-0063\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,1]]},"references-count":0,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,12,9]]},"published-print":{"date-parts":[[2015,10,1]]}},"alternative-id":["10.1515\/ms-2015-0063"],"URL":"https:\/\/doi.org\/10.1515\/ms-2015-0063","relation":{},"ISSN":["1337-2211","0139-9918"],"issn-type":[{"value":"1337-2211","type":"electronic"},{"value":"0139-9918","type":"print"}],"subject":[],"published":{"date-parts":[[2015,10,1]]}}}