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Search: id:A055228
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| 1, 1, 2, 3, 5, 11, 27, 71, 201, 603, 1905, 6318, 21887, 78912, 295260, 1143536, 4574144, 18859678, 80014835, 348776577, 1559776269, 7147792819, 33526120083, 160785623546, 787685471323, 3938427356615
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Axenovich's improvement to the Erdos strong Delta-system conjecture. Erdos and Rado called a family of sets {A1, A2, .., Ak} a strong Delta-system if all the intersections Ai INTERSECT Aj are identical, 1 <= i <= j <= k. Denoting by f(n,k) the smallest integer m for which every family of n-sets {A1, A2, .., Ak} contains k sets forming a strong Delta-system. Then Axenovich et al. proved f(n,3) < (n!)^((1/2) + epsilon)) < a(n) holds for every epsilon > 0, provided n is sufficiently large. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 29 2007
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REFERENCES
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M. Axenovich, D. Fon-Der-Flaass and A. Kostochka, On set systems without weak 3-Delta-subsystems, Discrete Math. 138(1995),57-62.
Bela Bollobas, Paul Erdos and His Mathematics, Am. Math. Monthly, 105(March 1998)3, p. 232.
P. Erdos and R. Rado, Intersection theorems for systems of finite sets, J. London Math. Soc. (2) 35(1960)85-90 and 44(1969)467-479.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..300
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FORMULA
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a(n) = A003059(A000142(n)). - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 29 2007
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CROSSREFS
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Cf. A000142, A003059.
Sequence in context: A006888 A009589 A098179 this_sequence A098642 A079447 A084865
Adjacent sequences: A055225 A055226 A055227 this_sequence A055229 A055230 A055231
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 21 2000
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EXTENSIONS
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A comment stating that one of the terms was wrong has been deleted - the terms are correct. - T. D. Noe, Apr 22 2009
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