{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T03:22:43Z","timestamp":1768447363377,"version":"3.49.0"},"reference-count":51,"publisher":"Wiley","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. London Math. Soc."],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1112\/jlms\/jdw067","type":"journal-article","created":{"date-parts":[[2016,11,9]],"date-time":"2016-11-09T10:39:10Z","timestamp":1478687950000},"page":"993-1018","source":"Crossref","is-referenced-by-count":16,"title":["The maximum product of weights of cross-intersecting families"],"prefix":"10.1112","volume":"94","author":[{"given":"Peter","family":"Borg","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2016,11,7]]},"reference":[{"key":"2016122100302230000_94.3.993.1","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1995.0092"},{"key":"2016122100302230000_94.3.993.2","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1006\/aama.1998.0588","article-title":"The diametric theorem in Hamming spaces: optimal anticodes","volume":"20","author":"Ahlswede","year":"1998","journal-title":"Adv. in Appl. Math."},{"key":"2016122100302230000_94.3.993.3","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0012-365X(85)90073-1","article-title":"Homomorphisms of 3-chromatic graphs","volume":"54","author":"Albertson","year":"1985","journal-title":"Discrete Math."},{"key":"2016122100302230000_94.3.993.4","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0166-218X(99)00069-4","article-title":"The Erd\u00f6s\u2013Ko\u2013Rado bound for the function lattice","volume":"95","author":"Bey","year":"1999","journal-title":"Discrete Appl. Math."},{"key":"2016122100302230000_94.3.993.5","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-004-0598-4"},{"key":"2016122100302230000_94.3.993.6","doi-asserted-by":"crossref","unstructured":"P. Borg , \u2018Intersecting and cross-intersecting families of labeled sets\u2019, Electron. J. Combin. 15 (2008) note paper N9.","DOI":"10.37236\/884"},{"key":"2016122100302230000_94.3.993.7","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.05.051"},{"key":"2016122100302230000_94.3.993.8","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdn062"},{"key":"2016122100302230000_94.3.993.9","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.jcta.2009.07.003","article-title":"Cross-intersecting families of permutations","volume":"117","author":"Borg","year":"2010","journal-title":"J. Combin. Theory Ser. A"},{"key":"2016122100302230000_94.3.993.10","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1137\/080731281","article-title":"Cross-intersecting families of partial permutations","volume":"24","author":"Borg","year":"2010","journal-title":"SIAM J. Disc. Math."},{"key":"2016122100302230000_94.3.993.11","unstructured":"P. Borg , \u2018Intersecting families of sets and permutations: a survey\u2019, Advances in mathematics research, vol. 16 (ed. A. R. Baswell; Nova Science Publishers, Inc., New York, 2011) 283\u2013299."},{"key":"2016122100302230000_94.3.993.12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2011.12.002"},{"key":"2016122100302230000_94.3.993.13","first-page":"69","article-title":"The maximum product of sizes of cross- $t$ -intersecting uniform families","volume":"60","author":"Borg","year":"2014","journal-title":"Australas. J. Combin."},{"key":"2016122100302230000_94.3.993.14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.06.029"},{"key":"2016122100302230000_94.3.993.15","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdu110"},{"key":"2016122100302230000_94.3.993.16","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.jcta.2009.11.010","article-title":"Multiple cross-intersecting families of signed sets","volume":"117","author":"Borg","year":"2010","journal-title":"J. Combin. Theory Ser. A"},{"key":"2016122100302230000_94.3.993.17","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1016\/S0195-6698(03)00078-7","article-title":"Intersecting families of permutations","volume":"24","author":"Cameron","year":"2003","journal-title":"European J. Combin."},{"key":"2016122100302230000_94.3.993.18","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(74)90013-2"},{"key":"2016122100302230000_94.3.993.19","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1137\/0604042","article-title":"The Erd\u00f6s\u2013Ko\u2013Rado theorem\u201422 years later","volume":"4","author":"Deza","year":"1983","journal-title":"SIAM J. Algebraic Discrete Methods"},{"key":"2016122100302230000_94.3.993.20","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/12.1.313"},{"key":"2016122100302230000_94.3.993.21","unstructured":"P. Frankl , \u2018The Erd\u00f6s\u2013Ko\u2013Rado theorem is true for $n = ckt$ \u2019, Proc. Fifth Hung. Comb. Coll. (North-Holland, Amsterdam, 1978) 365\u2013375."},{"key":"2016122100302230000_94.3.993.22","unstructured":"P. Frankl , \u2018The shifting technique in extremal set theory\u2019, Surveys in combinatorics (ed. C. Whitehead; Cambridge University Press, London\/New York, 1987) 81\u2013110."},{"key":"2016122100302230000_94.3.993.23","unstructured":"P. Frankl , \u2018Extremal set systems\u2019 (eds. R. L. Graham, M. Gr\u00f6tschel and L. Lov\u00e1sz), Handbook of Combinatorics 2 (Elsevier, Amsterdam, 1995) 1293\u20131329."},{"key":"2016122100302230000_94.3.993.24","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0097-3165(91)90031-B","article-title":"Beyond the Erd\u00f6s\u2013Ko\u2013Rado theorem","volume":"56","author":"Frankl","year":"1991","journal-title":"J. Combin. Theory Ser. A"},{"key":"2016122100302230000_94.3.993.25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2014.08.006"},{"key":"2016122100302230000_94.3.993.26","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s004930050045","article-title":"The Erd\u00f6s\u2013Ko\u2013Rado theorem for integer sequences","volume":"19","author":"Frankl","year":"1999","journal-title":"Combinatorica"},{"key":"2016122100302230000_94.3.993.27","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jcta.2016.06.017","article-title":"Invitation to intersection problems for finite sets","volume":"144","author":"Frankl","year":"2016","journal-title":"J. Combin. Theory Ser. A"},{"key":"2016122100302230000_94.3.993.28","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.ejc.2015.02.023","article-title":"A discrete isodiametric result: the Erd\u00f6s\u2013Ko\u2013Rado theorem for multisets","volume":"48","author":"F\u00fcredi","year":"2015","journal-title":"European J. Combin."},{"key":"2016122100302230000_94.3.993.29","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1112\/jlms\/s2-15.3.369","article-title":"An intersection theorem for a collection of families of subsets of a finite set","volume":"15","author":"Hilton","year":"1977","journal-title":"J. London Math. Soc. (2)"},{"key":"2016122100302230000_94.3.993.30","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/18.1.369"},{"key":"2016122100302230000_94.3.993.31","unstructured":"J. Hirschorn , \u2018Asymptotic upper bounds on the shades of $t$ -intersecting families\u2019, Preprint, 2008, arXiv:0808.1434 [math.CO]."},{"key":"2016122100302230000_94.3.993.32","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.08.041"},{"key":"2016122100302230000_94.3.993.33","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.08.028"},{"key":"2016122100302230000_94.3.993.34","doi-asserted-by":"publisher","DOI":"10.1007\/BF01897141"},{"key":"2016122100302230000_94.3.993.35","unstructured":"G. O. H. Katona , \u2018A theorem of finite sets\u2019, Theory of Graphs: Proceedings of the Colloquium Held at Tihany (Akad\u00e9miai Kiad\u00f3, Budapest, 1968) 187\u2013207."},{"key":"2016122100302230000_94.3.993.36","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0095-8956(72)90054-8","article-title":"A simple proof of the Erd\u00f6s\u2013Chao Ko\u2013Rado theorem","volume":"13","author":"Katona","year":"1972","journal-title":"J. Combin. Theory Ser. B"},{"key":"2016122100302230000_94.3.993.37","doi-asserted-by":"crossref","unstructured":"J. B. Kruskal , \u2018The number of simplices in a complex\u2019, Mathematical optimization techniques (University of California Press, Berkeley, California, 1963) 251\u2013278.","DOI":"10.1525\/9780520319875-014"},{"key":"2016122100302230000_94.3.993.38","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788667"},{"key":"2016122100302230000_94.3.993.39","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90065-4"},{"key":"2016122100302230000_94.3.993.40","doi-asserted-by":"crossref","unstructured":"K. Meagher and A. Purdy , \u2018An Erd\u00f6s\u2013Ko\u2013Rado theorem for multisets\u2019, Electron. J. Combin. 18 (2011) paper P220.","DOI":"10.37236\/707"},{"key":"2016122100302230000_94.3.993.41","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(82)90054-1"},{"key":"2016122100302230000_94.3.993.42","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00373-015-1551-4","article-title":"Cross-intersecting families of vectors","volume":"31","author":"Pach","year":"2015","journal-title":"Graphs Combin."},{"key":"2016122100302230000_94.3.993.43","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(86)90025-7"},{"key":"2016122100302230000_94.3.993.44","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdt101"},{"key":"2016122100302230000_94.3.993.45","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610703004356"},{"key":"2016122100302230000_94.3.993.46","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/j.jcta.2010.01.002","article-title":"On cross $t$ -intersecting families of sets","volume":"117","author":"Tokushige","year":"2010","journal-title":"J. Combin. Theory Ser. A"},{"key":"2016122100302230000_94.3.993.47","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1017\/S0963548313000138","article-title":"Cross $t$ -intersecting integer sequences from weighted Erd\u00f6s\u2013Ko\u2013Rado","volume":"22","author":"Tokushige","year":"2013","journal-title":"Combin. Prob. Comput."},{"key":"2016122100302230000_94.3.993.48","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1007\/s10801-012-0419-4","article-title":"The eigenvalue method for cross $t$ -intersecting families","volume":"38","author":"Tokushige","year":"2013","journal-title":"J. Algebr. Comb."},{"key":"2016122100302230000_94.3.993.49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2010.09.005"},{"key":"2016122100302230000_94.3.993.50","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579226"},{"key":"2016122100302230000_94.3.993.51","doi-asserted-by":"crossref","unstructured":"H. Zhang , \u2018Cross-intersecting families of labeled sets\u2019, Electron. J. Combin. 20 (2013) paper P17.","DOI":"10.37236\/3047"}],"container-title":["Journal of the London Mathematical Society"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T22:44:11Z","timestamp":1657665851000},"score":1,"resource":{"primary":{"URL":"http:\/\/doi.wiley.com\/10.1112\/jlms\/jdw067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,7]]},"references-count":51,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,12,21]]},"published-print":{"date-parts":[[2016,12]]}},"alternative-id":["10.1112\/jlms\/jdw067"],"URL":"https:\/\/doi.org\/10.1112\/jlms\/jdw067","relation":{},"ISSN":["0024-6107","1469-7750"],"issn-type":[{"value":"0024-6107","type":"print"},{"value":"1469-7750","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,7]]}}}