{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T07:55:51Z","timestamp":1649145351479},"reference-count":20,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1987,5,1]],"date-time":"1987-05-01T00:00:00Z","timestamp":546825600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":9574,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1987,5]]},"DOI":"10.1016\/0012-365x(87)90208-1","type":"journal-article","created":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T12:34:03Z","timestamp":1042806843000},"page":"23-46","source":"Crossref","is-referenced-by-count":4,"title":["Lattice parallelotopes and disjoint covering systems"],"prefix":"10.1016","volume":"65","author":[{"given":"M.A.","family":"Berger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Felzenbaum","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.S.","family":"Fraenkel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0012-365X(87)90208-1_BIB1","first-page":"69","article-title":"Improvements to two results concerning systems of residue sets","volume":"20","author":"Berger","year":"1985","journal-title":"Ars Combin."},{"key":"10.1016\/0012-365X(87)90208-1_BIB2","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1090\/S0273-0979-1986-15414-5","article-title":"New results about covering systems of residue sets","volume":"14","author":"Berger","year":"1986","journal-title":"Bull. Amer. Math. Soc."},{"key":"10.1016\/0012-365X(87)90208-1_BIB3","doi-asserted-by":"crossref","first-page":"375","DOI":"10.4064\/aa-45-4-375-379","article-title":"Necessary condition for the existence of an incongruent covering system with odd moduli","volume":"45","author":"Berger","year":"1986","journal-title":"Acta Arith."},{"key":"10.1016\/0012-365X(87)90208-1_BIB4","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0097-3165(86)90015-4","article-title":"Disjoint covering systems of rational Beatty sequences","volume":"42","author":"Berger","year":"1986","journal-title":"J. Combin. Theory Ser. A"},{"issue":"3","key":"10.1016\/0012-365X(87)90208-1_BIB5","doi-asserted-by":"crossref","first-page":"329","DOI":"10.4153\/CMB-1986-050-0","article-title":"The Herzog-Sch\u00f6nheim conjecture for finite nilpotent groups","volume":"29","author":"Berger","year":"1986","journal-title":"Canad. Math. Bull."},{"key":"10.1016\/0012-365X(87)90208-1_BIB6","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum and A.S. Fraenkel, improvements to the Newman-Zn\u00e1m result for disjoint covering systems, Acta Arith., in press.","DOI":"10.4064\/aa-50-1-1-13"},{"key":"10.1016\/0012-365X(87)90208-1_BIB7","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum and A.S. Fraenkel, Remark on the multiplicity of a partition of a group into cosets, Fund. Math., in press.","DOI":"10.4064\/fm-128-3-139-144"},{"key":"10.1016\/0012-365X(87)90208-1_BIB8","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF02579384","article-title":"A non-analytic proof of the Newman-Zn\u00e1m result for disjoint covering systems","volume":"6","author":"Berger","year":"1986","journal-title":"Combinatorica"},{"key":"10.1016\/0012-365X(87)90208-1_BIB9","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum and A.S. Fraenkel, Necessary condition for the existence of an incongruent covering system with odd moduli II, Acta Arith., in press.","DOI":"10.4064\/aa-48-1-73-79"},{"key":"10.1016\/0012-365X(87)90208-1_BIB10","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum, A.S. Fraenkel, Covers of product sets and the Korec-Zn\u00e1m result, J. European Combin., in press.","DOI":"10.1016\/S0195-6698(88)80037-4"},{"key":"10.1016\/0012-365X(87)90208-1_BIB11","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum and A.S. Fraenkel, Disjoint covering systems with precisely one multiple modulus, Acta Arith., in press.","DOI":"10.4064\/aa-50-2-171-182"},{"key":"10.1016\/0012-365X(87)90208-1_BIB12","doi-asserted-by":"crossref","unstructured":"M.A. Berger, A. Felzenbaum and A.S. Fraenkel, Mycielski-Sierpinski conjecture and Korec-Zn\u00e1m result, Colloq. Math., in press.","DOI":"10.4064\/cm-56-2-241-249"},{"key":"10.1016\/0012-365X(87)90208-1_BIB13","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0012-365X(76)90034-0","article-title":"On natural exactly covering systems of congruences having moduli occurring at most M times","volume":"14","author":"Burshtein","year":"1976","journal-title":"Discrete Math."},{"key":"10.1016\/0012-365X(87)90208-1_BIB14","article-title":"On covering sets of congruences","author":"Dewar","year":"1972","journal-title":"Ph.D. Dissertation, Univ. of Southern California"},{"key":"10.1016\/0012-365X(87)90208-1_BIB15","series-title":"An Introduction to the Theory of Numbers","author":"Hardy","year":"1979"},{"key":"10.1016\/0012-365X(87)90208-1_BIB16","article-title":"Covering sets of the integers","author":"Krukenberg","year":"1971"},{"key":"10.1016\/0012-365X(87)90208-1_BIB17","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF01350330","article-title":"Roots of unity and covering sets","volume":"191","author":"Newman","year":"1971","journal-title":"Math. Ann."},{"key":"10.1016\/0012-365X(87)90208-1_BIB18","article-title":"Results and Problems on Covering Systems of Residue Classes","volume":"Heft 150","author":"Porubsk\u00fd","year":"1981"},{"key":"10.1016\/0012-365X(87)90208-1_BIB19","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0012-365X(86)90079-8","article-title":"Exact coverings of the integers by arithmetic progressions","volume":"59","author":"Simpson","year":"1986","journal-title":"Discrete Math."},{"key":"10.1016\/0012-365X(87)90208-1_BIB20","first-page":"221","article-title":"On exactly covering systems of arithmetic sequences","volume":"Vol. 2","author":"Zn\u00e1m","year":"1970"}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X87902081?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X87902081?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,30]],"date-time":"2019-03-30T07:54:30Z","timestamp":1553932470000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0012365X87902081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,5]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1987,5]]}},"alternative-id":["0012365X87902081"],"URL":"https:\/\/doi.org\/10.1016\/0012-365x(87)90208-1","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1987,5]]}}}