Zusammenfassung
Viele Familien von Zahlen treten bei vielen verschiedenartigen mathematischen Problemen immer wieder auf: Oft tragen sie die Namen der Mathematiker, von denen sie untersucht worden sind. In diesem Kapitel werden wir Bell und Stirling, Ramanujan, Catalan, Bernoulli und Euler, Fibonacci und Lucas begegnen.
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Literaturhinweise
VI. Arnold: Bernoulli-Euler updown numbers associated with function singular- ities, their combinatorics and arithmetics, Duke Math. J. 63 (1991): 537–555.
VI. Arnold: Snake calculus and combinatorics of Bernoulli, Euler and Springer numbers for Coxeter groups. Russian Math. Surveys 47 (1992): 3–45.
M.D. Atkinson: How to compute the series expansions of secx and tanx. Amer. Math. Monthly 93 (1986): 387–389.
E.R. Berlekamp, J.H. Conway, and R.K. Guy: Winning Ways for your Mathematical Plays, Academic Press, 1982, 475–478, 501.
N.G. de Bruijn, B.J.M. Morselt: A note on plane trees. J. Combin. Theory 2 (1967): 27–34.
B.L. Burrows, R.F. Talbot: Sums of powers of integers. Amer. Math. Monthly 91 (1984): 394–403.
J.H. Conway, H.S.M. Coxeter, Triangulated polygons and frieze patterns Math. Gaz. 57(1973): 87–94, 175–183; MR51 # 1254–5.
A.W. F. Edwards: A quick route to sums of powers. Amer. Math. Monthly 93 (1986): 451–455.
Antal E. Fekete: Apropos two notes on notation. Amer. Math. Monthly 101 (1994): 771–778.
Johann Wolfgang von Goethe: Versuch, die Metamorphose der Pflanzen zu erklären, Gotha, 1790.
H.W. Gould: Bell & Catalan Numbers: Research Bibliography of Two Special Number Sequences, Sixth Edition, Morgantown, WV, 1985.
Ronald L. Graham, Donald E. Knuth, Oren Patashnik: Concrete Mathematics, A Foundation for Computer Science, Addison-Wesley, Reading, MA, 1989.
J. Karamata: Theoremes sur la sommabilite exponentielle et d’autres somma- bilites s’y rattachant. Mathematica (Cluj), 9 (1935): 164–178.
A.A. Kirillow: Variations on the triangular theme in S.G. Gindikin & E.B. Vinberg (Hrsg.). E.B. Dynkin Seminar on Lie Groups. Amer. Math. Soc., 1995.
Donald E. Knuth: Two notes on notation, Amer. Math. Monthly 99 (1992): 403–422.
D.E. Knuth, T.J. Buckholtz: Computation of tangent, Euler andBernoulli numbers, Math. Comput. 21 (1967): 663–688.
Mark Krusemeyer: A parenthical note (to a paper of Richard Guy). Math. Mag. 69(1996).
Michael J. Kuchinski: Catalan Structures and Correspondences, M. Sc. Thesis, West Virginia University, 1977.
Luo Jian-Jin: An Tu Ming, the first discoverer of the Catalan numbers. Nei- menggu Daxue Xuebo 19(1988): 239–245; MR 90: 01007.
J. Miliar, N.J.A. Sloane, N.E. Young: A new operation on sequences: The boustrophedon transform, J. Combin. Theory, Ser. A 76 (1996): 44–54.
Th. Motzkin: Relations between hypersurface cross-ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associativeproducts. Bull. Amer. Math. Soc. 54(1948): 352–360; MR9: 489–490.
C.D. Oakley, R.J. Wisner: Flexagons. Amer. Math. Monthly 64(1975): 143–154; MR 19: 241b.
Przemyslaw Prusinkiewicz, Aristid Lindenmayer: The Algorithmic Beauty of Plants, with James S. Hanan, F. David Fracchia, Deborah R. Fowler, Martin J.M. de Boer & Lynn Mercer, Springer-Verlag, 1990.
H. Rademacher: On the partition function p(n). Proc. London Math. Soc. (2), 43 (1937): 241–254.
Ibrahim A. Salama, Lawrence L. Kupper: A geometric interpretation for the Eulerian numbers. Amer. Math. Monthly 93 (1986): 51–52.
J.O. Shallit: E2972. Another appearance of the Catalan numbers. Amer. Math. Monthly 89 (1982): 698;
J.O. Shallit: Solution David M. Wells, 93 (1986): 217–218.
Ian Stewart: Mathematical Recreations: Daisy; Daisy, give meyour answer, do. Sei. Amer.: 272 (Jan 1995): 96–99.
Peter Guthrie Täte in: Proc. Royal Soc. Edinburgh VII (1870–71): 391–394.
D’Arcy Wentworth Thompson: On Growth and Form, Cambridge Univ. Press, 1952.
C.W. Wardlaw: Organization and Evolution in Plants, Longmans Green, 1965.
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Conway, J.H., Guy, R.K. (1997). Berühmte Familien von Zahlen. In: Zahlenzauber. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6084-0_4
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