Oberschelp, W. Kombinatorische Anzahlbestimmungen in Relationen. (German) Zbl 0155.35002 Math. Ann. 174, 53-78 (1967). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 20 Documents Keywords:set theory PDFBibTeX XMLCite \textit{W. Oberschelp}, Math. Ann. 174, 53--78 (1967; Zbl 0155.35002) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Number of graphs on n unlabeled nodes. Number of symmetric reflexive relations on n nodes: (1/2)*A000666. Number of unlabeled simple digraphs with n nodes. Number of binary relations on n unlabeled points. Number of relations with 3 arguments on n nodes. Number of relations on an infinite set. Number of graphs with n edges. Number of 3-uniform hypergraphs on n unlabeled nodes, or equivalently number of relations with 3 arguments on n nodes. Number of symmetric relations on n nodes. Half the number of binary relations on n unlabeled points. References: [1] Bollobas, B.: On generalized graphs. Acta Math. Hung.16, 447-452 (1965). · Zbl 0138.19404 [2] De Bruijn, N. G.: Polay’s theory of counting. In:Beckenbach (ed.), Applied combinatorial mathematics, p. 144-184. New York-London-Sidney: Wiley 1964. [3] Cayley, A.: On the analytical forms called trees. Am. J. Math.4, 266-268 (1881). · JFM 13.0867.02 [4] Davis, R. L.: The number of structures of finite relations. Proc. Am. Math. Soc.4, 486-495 (1953). · Zbl 0051.24702 [5] Ford, G. W., andG. E. Uhlenbeck: Combinatorial problems in the theory of graphs, I bis IV. Proc. Nat. Acad. Sci. U.S.42, 122-128, 203-208 (mitR. Z. Normann), 529-535 (1956) und43, 163-167 (1957). · Zbl 0071.39101 [6] Harary, F.: The number of linear, directed, rooted and connected graphs. Trans. Am. Math. Soc.78, 445-463 (1955). · Zbl 0065.16702 [7] ?? Note on an enumeration theorem of Davis and Slepian. Michigan J. Math.3, 149-153 (1955/56). · Zbl 0074.25006 [8] ?? Note on Carnap’s relational asymptotic relative frequencies. J. Symb. Logic23, 257-260 (1958). [9] ?? Unsolved problems in the enumeration of graphs. Publ. Math. Inst. Hung. Acad. Sc. Ser. A5, 63-95 (1960). · Zbl 0095.16902 [10] Henze, H. R., andC. M. Blair: The number of structural isomers of the more important types of aliphatic compounds. J. Am. Chem. Soc.56, 157 (1934). [11] Lunn, A. C., andJ. K. Senior: Isomerism and configuration. J. Phys. Chem.33, 1027-1079 (1929). [12] Lupanov, O. B.: Über asymptotische Abschätzungen der Zahl von Graphen und Netzen mitn Kanten. (R): Prob. Kibernet.4, 5-21 (1960) (Russ.). (D): Dt. Übersetzung in: Probl. Kybern.4, 3-22 (1964). [13] Oberschelp, W.: Zykelindices induzierter Permutationsgruppen. Nachr. Öster. Math. Ges.19 (1965): Sonderheft VI. Öster. Math. Kongr. Graz 1964, S. 18. [14] ?? Kombinatorik. In: Fischer Lexikon, Bd. 29/2 (Mathematik 2), Hrsg.v. H. Behnke undH. Tietz, S. 142-168. Frankfurt: Fischer 1966. [15] Polya, G.: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta Math.68, 145-254 (1937). · Zbl 0017.23202 [16] Riddell, R. J., andG. E. Uhlenbeck: On the theory of the virial development of state of monoatomic gases. J. Chem. Phys.21, 2056-2064 (1953). [17] Riordan, J.: An introduction to combinatorial analysis, 244 S. New York: Wiley 1958. · Zbl 0078.00805 [18] Slepian, D.: Number of types of linear graphs. Techn. Mem. Bell Teleph. Lab., June 22, 1953. · Zbl 0051.24802 [19] Uhlenbeck, G. E., andG. W. Ford: Theory of linear graphs with application to the theory of the virial development of the properties of gases. In: Studies in Statistical Mechanics1, 123-211 (1962) (Hrsg.J. de Boer undG. E. Uhlenbeck). · Zbl 0116.45509 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.