{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T23:58:12Z","timestamp":1649030292408},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T00:00:00Z","timestamp":1573257600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T00:00:00Z","timestamp":1573257600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s00493-019-2429-5","type":"journal-article","created":{"date-parts":[[2019,11,9]],"date-time":"2019-11-09T05:15:50Z","timestamp":1573276550000},"page":"1281-1315","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hyper-Atoms Applied to the Critical Pair Theory"],"prefix":"10.1007","volume":"39","author":[{"given":"Yahya O.","family":"Hamidoune","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,11,9]]},"reference":[{"key":"2429_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00222-008-0157-3","volume":"176","author":"R Aharoni","year":"2009","unstructured":"R. Aharoni and E. Berger: Menger\u2019s Theorem for Infinite Graphs, Invent. Math.176 (2009), 1\u201362.","journal-title":"Invent. Math."},{"key":"2429_CR2","doi-asserted-by":"publisher","first-page":"915","DOI":"10.5802\/aif.2374","volume":"58","author":"E Balandraud","year":"2008","unstructured":"E. Balandraud: Un nouveau point de vue isop\u00e9rimetrique appliqu\u00e9 au th\u00e9or\u00e8me de Kneser, Ann. Inst. Fourier58 (2008), 915\u2013943.","journal-title":"Ann. Inst. Fourier"},{"key":"2429_CR3","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1016\/j.ejc.2004.06.011","volume":"26","author":"D Grynkiewicz","year":"2005","unstructured":"D. Grynkiewicz: Quasi-periodic decompositions and the Kemperman\u2019s structure theorem, European J. Combin.26 (2005), 559\u2013575.","journal-title":"European J. Combin."},{"key":"2429_CR4","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1112\/S0025579300000966","volume":"55","author":"D Grynkiewicz","year":"2009","unstructured":"D. Grynkiewicz: A step beyond Kemperman\u2019s structure theorem, Mathematika55 (2009), 67\u2013114.","journal-title":"Mathematika"},{"key":"2429_CR5","doi-asserted-by":"crossref","unstructured":"D. Grynkiewicz: Structural Additive Theory, Developments in Mathematics 30, Springer (2013).","DOI":"10.1007\/978-3-319-00416-7"},{"key":"2429_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0095-8956(81)90085-X","volume":"30","author":"Y O Hamidoune","year":"1981","unstructured":"Y. O. Hamidoune: Quelques probl\u00e8mes de connexit\u00e9 dans les graphes orient\u00e9s, J. Comb. Theory, Ser. B30 (1981), 1\u201310.","journal-title":"J. Comb. Theory, Ser. B"},{"key":"2429_CR7","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S0195-6698(84)80034-7","volume":"5","author":"Y O Hamidoune","year":"1984","unstructured":"Y. O. Hamidoune: On the connectivity of Cayley digraphs, Europ. J. Combinatorics, 5 (1984), 309\u2013312.","journal-title":"Europ. J. Combinatorics"},{"key":"2429_CR8","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1006\/eujc.1995.0113","volume":"18","author":"Y O Hamidoune","year":"1997","unstructured":"Y. O. Hamidoune: Subsets with small sums in abelian groups I: The Vosper property, European J. Combin.18 (1997), 541\u2013556.","journal-title":"European J. Combin."},{"key":"2429_CR9","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1006\/jabr.1996.0028","volume":"179","author":"Y O Hamidoune","year":"1996","unstructured":"Y. O. Hamidoune: An isoperimetric method in additive theory, J. Algebra179 (1996), 622\u2013630.","journal-title":"J. Algebra"},{"key":"2429_CR10","doi-asserted-by":"publisher","first-page":"97","DOI":"10.4064\/aa96-2-1","volume":"96","author":"Y O Hamidoune","year":"2000","unstructured":"Y. O. Hamidoune; Some results in Additive number Theory I: The critical pair Theory, Acta Arith.96 (2000), 97\u2013119.","journal-title":"Acta Arith."},{"key":"2429_CR11","doi-asserted-by":"publisher","first-page":"2007","DOI":"10.5802\/aif.2404","volume":"58","author":"Y O Hamidoune","year":"2008","unstructured":"Y. O. Hamidoune: Some additive applications of the isopermetric approach, Annales de l\u2019 Institut Fourier58 (2008), 2007\u20132036.","journal-title":"Annales de l\u2019 Institut Fourier"},{"key":"2429_CR12","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s00014-003-0786-5","volume":"79","author":"Y O Hamidoune","year":"2004","unstructured":"Y. O. Hamidoune and A. Plagne: A new critical pair theorem applied to sum-free sets, Comment. Math. Helv.79 (2004), 183\u2013207.","journal-title":"Comment. Math. Helv."},{"key":"2429_CR13","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1007\/BF02546525","volume":"103","author":"J H B Kemperman","year":"1960","unstructured":"J. H. B. Kemperman: On small sumsets in Abelian groups, Acta Math.103 (1960), 66\u201388.","journal-title":"Acta Math."},{"key":"2429_CR14","doi-asserted-by":"publisher","first-page":"125","DOI":"10.5802\/jtnb.618","volume":"20","author":"Y O Hamidoune","year":"2008","unstructured":"Y. O. Hamidoune, O. Serra and G. Z\u00e9mor: One some subgroup chains related to Kneser\u2019s Theorem, J. Th\u00e9or. Nr. Bordx.20 (2008), 125\u2013130.","journal-title":"J. Th\u00e9or. Nr. Bordx."},{"key":"2429_CR15","first-page":"255","volume":"44","author":"R A Lee","year":"1974","unstructured":"R. A. Lee: Proving Kneser\u2019s theorem for finite groups by another e-transform, Proc. Amer. Math. Soc.44 (1974), 255\u2013258.","journal-title":"Proc. Amer. Math. Soc."},{"key":"2429_CR16","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1142\/S1793042106000620","volume":"2","author":"V F Lev","year":"2006","unstructured":"V. F. Lev: Critical pairs in abelian groups and Kemperman\u2019s structure theorem, Int. J. Number Theory2 (2006), 379\u2013396.","journal-title":"Int. J. Number Theory"},{"key":"2429_CR17","doi-asserted-by":"crossref","unstructured":"M. B. Nathanson: Additive Number Theory. Inverse problems and the geometry of sumsets, Grad. Texts in Math. 165, Springer, 1996.","DOI":"10.1007\/978-1-4757-3845-2"},{"key":"2429_CR18","doi-asserted-by":"crossref","unstructured":"T. Tao and V. H. Vu: Additive Combinatorics, Cambridge Studies in Advanced Mathematics 105 (2006), Cambridge University Press.","DOI":"10.1017\/CBO9780511755149"},{"key":"2429_CR19","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1112\/jlms\/s1-31.2.200","volume":"31","author":"G Vosper","year":"1956","unstructured":"G. Vosper: The critical pairs of subsets of a group of prime order, J. London Math. Soc.31 (1956), 200\u2013205.","journal-title":"J. London Math. Soc."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-2429-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-019-2429-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-019-2429-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,8]],"date-time":"2020-11-08T00:35:36Z","timestamp":1604795736000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-019-2429-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,9]]},"references-count":19,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["2429"],"URL":"https:\/\/doi.org\/10.1007\/s00493-019-2429-5","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,9]]},"assertion":[{"value":"15 August 2007","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2014","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}