{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:05:28Z","timestamp":1740107128034,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T00:00:00Z","timestamp":1726876800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T00:00:00Z","timestamp":1726876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s00373-024-02835-z","type":"journal-article","created":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T14:01:33Z","timestamp":1726927293000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Maximum Sum of Sizes of Non-Empty Cross t-Intersecting Families"],"prefix":"10.1007","volume":"40","author":[{"given":"Shuang","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-8112-4823","authenticated-orcid":false,"given":"Dehai","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deping","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,21]]},"reference":[{"issue":"2","key":"2835_CR1","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1006\/eujc.1995.0092","volume":"18","author":"R Ahlswede","year":"1997","unstructured":"Ahlswede, R., Khachatrian, L.H.: The complete intersection theorem for systems of finite sets. Eur. J. Combin. 18(2), 125\u2013136 (1997)","journal-title":"Eur. J. Combin."},{"issue":"3","key":"2835_CR2","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1007\/BF01388470","volume":"76","author":"M Aschbacher","year":"1984","unstructured":"Aschbacher, M.: On the maximal subgroups of the finite classical groups. Invent. Math. 76(3), 469\u2013514 (1984)","journal-title":"Invent. Math."},{"issue":"11","key":"2835_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2022.112981","volume":"345","author":"P Borg","year":"2022","unstructured":"Borg, P., Feghali, C.: The maximum sum of sizes of cross-intersecting families of subsets of a set. Discr. Math. 345(11), 112981 (2022)","journal-title":"Discr. Math."},{"issue":"4","key":"2835_CR4","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1137\/0604042","volume":"4","author":"M Deza","year":"1983","unstructured":"Deza, M., Frankl, P.: The Erd\u0151s\u2013Ko\u2013Rado theorem\u2013$$22$$ years later. SIAM J. Algebr. Discr. Methods 4(4), 419\u2013431 (1983)","journal-title":"SIAM J. Algebr. Discr. Methods"},{"issue":"12","key":"2835_CR5","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1093\/qmath\/12.1.313","volume":"2","author":"P Erd\u0151s","year":"1961","unstructured":"Erd\u0151s, P., Ko, C., Rado, R.: Intersection theorems for systems of finite sets. Quart. J. Math. Oxf. 2(12), 313\u2013320 (1961)","journal-title":"Quart. J. Math. Oxf."},{"key":"2835_CR6","first-page":"365","volume":"18","author":"P Frankl","year":"1978","unstructured":"Frankl, P.: The Erd\u0151s-Ko-Rado theorem is true for $$n=ckt$$. Coll. Math. Soc. J. Bolyai 18, 365\u2013375 (1978)","journal-title":"Coll. Math. Soc. J. Bolyai"},{"issue":"2","key":"2835_CR7","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/S0195-6698(85)80009-3","volume":"6","author":"P Frankl","year":"1985","unstructured":"Frankl, P., Graham, R.L.: Intersection theorems for vector spaces. Eur. J. Combin. 6(2), 183\u2013187 (1985)","journal-title":"Eur. J. Combin."},{"key":"2835_CR8","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.dam.2023.09.011","volume":"342","author":"P Frankl","year":"2024","unstructured":"Frankl, P., Liu, E.L.L., Wang, J., Yang, Z.: Non-trivial $$t$$-intersecting separated families. Discr. Appl. Math. 342, 124\u2013137 (2024)","journal-title":"Discr. Appl. Math."},{"issue":"1","key":"2835_CR9","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0097-3165(92)90054-X","volume":"61","author":"P Frankl","year":"1992","unstructured":"Frankl, P., Tokushige, N.: Some best possible inequalities concerning cross-intersecting families. J. Combin. Theory Ser. A 61(1), 87\u201397 (1992)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"2","key":"2835_CR10","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/0097-3165(86)90063-4","volume":"43","author":"P Frankl","year":"1986","unstructured":"Frankl, P., Wilson, R.M.: The Erd\u0151s-Ko-Rado theorem for vector spaces. J. Combin. Theory Ser. A 43(2), 228\u2013236 (1986)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"3","key":"2835_CR11","doi-asserted-by":"publisher","first-page":"1447","DOI":"10.1112\/blms.12803","volume":"55","author":"P Gupta","year":"2023","unstructured":"Gupta, P., Mogge, Y., Piga, S., Sch\u00fclke, B.: $$r$$-cross $$t$$-intersecting families via necessary intersection points. Bull. Lond. Math. Soc. 55(3), 1447\u20131458 (2023)","journal-title":"Bull. Lond. Math. Soc."},{"issue":"18","key":"2835_CR12","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1093\/qmath\/18.1.369","volume":"2","author":"AJW Hilton","year":"1967","unstructured":"Hilton, A.J.W., Milner, E.C.: Some intersection theorems for systems of finite sets. Quart. J. Math. Oxf. Ser. 2(18), 369\u2013384 (1967)","journal-title":"Quart. J. Math. Oxf. Ser."},{"key":"2835_CR13","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/0097-3165(75)90037-0","volume":"18","author":"WN Hsieh","year":"1975","unstructured":"Hsieh, W.N.: Families of intersecting finite vector spaces. J. Combinatorial Theory Ser. A 18, 252\u2013261 (1975)","journal-title":"J. Combinatorial Theory Ser. A"},{"issue":"1","key":"2835_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0012-365X(75)90091-6","volume":"12","author":"WN Hsieh","year":"1975","unstructured":"Hsieh, W.N.: Intersection theorems for systems of finite vector spaces. Discr. Math. 12(1), 1\u201316 (1975)","journal-title":"Discr. Math."},{"issue":"12","key":"2835_CR15","doi-asserted-by":"publisher","first-page":"30910","DOI":"10.3934\/math.20231581","volume":"8","author":"ELL Liu","year":"2023","unstructured":"Liu, E.L.L.: The maximum sum of the sizes of cross $$t$$-intersecting separated families. AIMS Math. 8(12), 30910\u201330921 (2023)","journal-title":"AIMS Math."},{"issue":"2","key":"2835_CR16","doi-asserted-by":"publisher","first-page":"1108","DOI":"10.1016\/j.jalgebra.2005.12.020","volume":"304","author":"B Newton","year":"2006","unstructured":"Newton, B., Benesh, B.: A classification of certain maximal subgroups of symmetric groups. J. Algebra 304(2), 1108\u20131113 (2006)","journal-title":"J. Algebra"},{"issue":"5","key":"2835_CR17","doi-asserted-by":"publisher","first-page":"903","DOI":"10.1016\/j.jcta.2005.08.006","volume":"113","author":"H Tanaka","year":"2006","unstructured":"Tanaka, H.: Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs. J. Combin. Theory Ser. A 113(5), 903\u2013910 (2006)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"1","key":"2835_CR18","doi-asserted-by":"publisher","first-page":"43","DOI":"10.11650\/twjm\/1500404632","volume":"11","author":"J Wang","year":"2007","unstructured":"Wang, J., Zhang, H.: Normalized matching property of a class of subspace lattices. Taiwan. J. Math. 11(1), 43\u201350 (2007)","journal-title":"Taiwan. J. Math."},{"issue":"1","key":"2835_CR19","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.jcta.2012.07.005","volume":"120","author":"J Wang","year":"2013","unstructured":"Wang, J., Zhang, H.: Nontrivial independent sets of bipartite graphs and cross-intersecting families. J. Combin. Theory Ser. A 120(1), 129\u2013141 (2013)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"2","key":"2835_CR20","first-page":"341","volume":"19","author":"Y Wang","year":"1999","unstructured":"Wang, Y.: On a class of subspace lattices. J. Math. Res. Expos. 19(2), 341\u2013348 (1999)","journal-title":"J. Math. Res. Expos."},{"key":"2835_CR21","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/BF02579226","volume":"4","author":"RM Wilson","year":"1984","unstructured":"Wilson, R.M.: The exact bound in the Erd\u0151s\u2013Ko\u2013Rado theorem. Combinatorica 4, 247\u2013257 (1984)","journal-title":"Combinatorica"}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-024-02835-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-024-02835-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-024-02835-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,24]],"date-time":"2024-10-24T15:04:32Z","timestamp":1729782272000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-024-02835-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,21]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["2835"],"URL":"https:\/\/doi.org\/10.1007\/s00373-024-02835-z","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2024,9,21]]},"assertion":[{"value":"1 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 August 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 September 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"103"}}