{"title":"Minimal completely separating systems","authors":"Joel Spencer","doi":"10.1016/S0021-9800(70)80038-2","DOIUrl":"10.1016/S0021-9800(70)80038-2","url":null,"abstract":"<div><p>The minimal size of a completely separating system on <em>n</em> points is found.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 4","pages":"Pages 446-447"},"PeriodicalIF":0.0,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80038-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84222543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the extreme points of a certain convex polytope","authors":"M. Katz","doi":"10.1016/S0021-9800(70)80034-5","DOIUrl":"10.1016/S0021-9800(70)80034-5","url":null,"abstract":"<div><p>The convex polytope of all stochastic and symmetric matrices is considered and its extreme points are determined. A method is given for counting these extreme points.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 4","pages":"Pages 417-423"},"PeriodicalIF":0.0,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80034-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86456789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sur la croissance du nombre de systèmes triples de Steiner non lsomorphes","authors":"Jean Doyen","doi":"10.1016/S0021-9800(70)80035-7","DOIUrl":"10.1016/S0021-9800(70)80035-7","url":null,"abstract":"<div><p>Nous montrons que le nombre de systèmes triples de Steiner non isomorphes d'ordre <em>n</em> qui contiennent un sous-système d'ordre 7 tend vers l'infini avec <em>n</em>, ce qui généralise un résultat récent de Assmus et Mattson.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 4","pages":"Pages 424-441"},"PeriodicalIF":0.0,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80035-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80265259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Réarrangements de fonctions et dénombrement","authors":"Dominique Foata , Aimé Fuchs","doi":"10.1016/S0021-9800(70)80031-X","DOIUrl":"10.1016/S0021-9800(70)80031-X","url":null,"abstract":"<div><p>On donne l'énoncé d'un théorème sur les réarrangements d'applications d'un ensemble fini dans lui-même, qui généralise un résultat connu sur les permutations, et qui permet de retrouver le dénombrement des classes d'applications ultimement idempotentes et indécomposables, ainsi que celui des arbres de <em>n</em> sommets et des graphes connexes de <em>n</em> arêtes et <em>n</em> sommets.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 4","pages":"Pages 361-375"},"PeriodicalIF":0.0,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80031-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81509134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Common transversals and strong exchange systems","authors":"Richard A. Brualdi","doi":"10.1016/S0021-9800(70)80084-9","DOIUrl":"10.1016/S0021-9800(70)80084-9","url":null,"abstract":"<div><p>We investigate properties of common transversals of two families of sets. Some structure theorems are proved, and we settle affirmatively a conjecture of L. Mirsky and H. Perfect concerning the existence of a common transversal for two families of sets.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 307-329"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80084-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89235980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bottleneck extrema","authors":"Jack Edmonds , D.R. Fulkerson","doi":"10.1016/S0021-9800(70)80083-7","DOIUrl":"https://doi.org/10.1016/S0021-9800(70)80083-7","url":null,"abstract":"<div><p>Let <em>E</em> be a finite set. Call a family of mutually noncomparable subsets of <em>E</em> a clutter on <em>E</em>. It is shown that for any clutter <span><math><mi>ℛ</mi></math></span> on <em>E</em>, there exists a unique clutter <span><math><mi>ℒ</mi></math></span> on <em>E</em> such that, for any function <em>f</em> from <em>E</em> to real numbers,</p><p><span><span><span><math><mrow><mtable><mtr><mtd><mrow><mo>min</mo><mo></mo><mo>max</mo><mo></mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo></mrow></mtd></mtr><mtr><mtd><mrow><mo>R</mo><msup><mo>∈</mo><mi>ℛ</mi></msup><mo>x</mo><msup><mo>∈</mo><mo>R</mo></msup></mrow></mtd></mtr></mtable><mtable><mtr><mtd><mrow><mo>max</mo><mo></mo><mo>min</mo><mo></mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>S</mo><msup><mo>∈</mo><mi>ℒ</mi></msup><mo>x</mo><msup><mo>∈</mo><mo>S</mo></msup></mrow></mtd></mtr></mtable></mrow></math></span></span></span></p><p>Specifically, <span><math><mi>ℒ</mi></math></span> consists of the minimal subsets of <em>E</em> that have non-empty intersection with every member of <span><math><mi>ℛ</mi></math></span>. The pair <span><math><mrow><mrow><mo>(</mo><mrow><mi>ℛ</mi><mo>,</mo><mi>ℒ</mi></mrow><mo>)</mo></mrow></mrow></math></span> is called a blocking system on <em>E</em>. An algorithm is described and several examples of blockings systems are discussed.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 299-306"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80083-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137271922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two Mal'cev-type theorems in universal algebra","authors":"G. Grätzer","doi":"10.1016/S0021-9800(70)80086-2","DOIUrl":"10.1016/S0021-9800(70)80086-2","url":null,"abstract":"<div><p>Patterned after theorems of Mal'cev and Jónsson, certain types of conditions for equational classes of algebras are named “Mal'cev type.” Regularity and weak regularity of equational classes of algebras are proved to be of “Mal'cev type.”</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 334-342"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80086-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77889496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A packing theory","authors":"David A. Klarner","doi":"10.1016/S0021-9800(70)80080-1","DOIUrl":"10.1016/S0021-9800(70)80080-1","url":null,"abstract":"<div><p>Let <em>A</em> be a set and let <span><math><mi>A</mi></math></span> be a collection of subsets of <em>A</em>. Conditions are given that must hold if a partition of <em>A</em> is a subset of <span><math><mi>A</mi></math></span>. The main idea presented is a generalization of several methods that have been used to prove certain packing theorems.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 272-278"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80080-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72690206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the number of orthogonal latin squares","authors":"Haim Hanani","doi":"10.1016/S0021-9800(70)80079-5","DOIUrl":"10.1016/S0021-9800(70)80079-5","url":null,"abstract":"<div><p>Let <em>N(n)</em> be the maximal number of mutually orthogonal Latin squares of order <em>n</em> and let <em>n<sub>r</sub></em> be the smallest integer such that <em>N(n)≥r</em> for every <em>n>n<sub>r</sub></em>. It is known that <em>N(n)</em>→∞ as <em>n</em>→∞ and that <em>n</em><sub>2</sub>=6. A proof is given for <em>n</em><sub>3</sub>≤51, <em>n</em><sub>5</sub>≤62 and <em>n</em><sub>29</sub>≤34, 115, 553.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 247-271"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80079-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88181860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Enumeration of certain binary matrices","authors":"Douglas E. Jackson, R.C. Entringer","doi":"10.1016/S0021-9800(70)80082-5","DOIUrl":"10.1016/S0021-9800(70)80082-5","url":null,"abstract":"<div><p>An <em>m×n</em> (0, 1) matrix (<em>a<sub>ij</sub></em>) is said to be a * matrix iff <em>a<sub>ij</sub></em>=1 implies <em>a<sub>i′j′</sub></em>=1 for all (<em>i′, j′</em>) satisfying 1≤<em>i′<i, 1≤j′≤j</em>. * matrices with certain additional restrictions are counted and enumerations of random walks and decision patterns are obtained.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 291-298"},"PeriodicalIF":0.0,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80082-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82448924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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