{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:36:52Z","timestamp":1759639012794},"reference-count":4,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> In this paper, we present a new proof for a well-known inequality, conjectured by Zassenhaus in 1947 and proved independently by Groemer in 1960 and Oler in 1961. The inequality gives an upper bound for the number of nonoverlapping unit discs whose centers can be packed into a compact convex region, and recently obtains a lot of applications in study of sensor networks. <\/jats:p>","DOI":"10.1142\/s1793830912500140","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T14:55:53Z","timestamp":1340117753000},"page":"1250014","source":"Crossref","is-referenced-by-count":15,"title":["A NEW PROOF FOR ZASSENHAUS\u2013GROEMER\u2013OLER INEQUALITY"],"prefix":"10.1142","volume":"04","author":[{"given":"QINGHAI","family":"LIU","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, China"}]},{"given":"XIANG","family":"LI","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"}]},{"given":"LIDONG","family":"WU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}]},{"given":"HAI","family":"DU","sequence":"additional","affiliation":[{"name":"Xi'an Jiaotong University, China"}]},{"given":"ZHAO","family":"ZHANG","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi, China"}]},{"given":"WEILI","family":"WU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}]},{"given":"XIAODONG","family":"HU","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"}]},{"given":"YINFENG","family":"XU","sequence":"additional","affiliation":[{"name":"Xi'an Jiaotong University, China"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1969-096-7"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01159721"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02559533"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1961-10614-9"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500140","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:42:05Z","timestamp":1565131325000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":4,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S1793830912500140"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500140","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}