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An introduction to finite fibonomial calculus

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EN
Abstrakty
EN
This is an indicatory presentation of main definitions and theorems of Fibonomial Calculus which is a special case of ψ-extented Rota's finite operator calculus [7].
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
5
Strony
754-766
Opis fizyczny
Daty
wydano
2004-10-01
online
2004-10-01
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autor
Bibliografia
  • [1] B. Bondarienko: Generalized Pascal Triangles and Pyramids- Their Fractals, graphs and Applications, A reproduction by the Fibonacci Association 1993, Santa Clara University, Santa Clara, CA.
  • [2] R.L. Graham, D.E. Knuth and O. Patashnik: Concrete mathematics. A Foundation for Computer Science, Addison-Wesley Publishing Company, Inc., Massachusetts, 1994.
  • [3] C. Graves: “On the principles which regulate the interchange of symbols in certain symbolic equations”, Proc. Royal Irish Academy, Vol. 6, (1853–1857), pp. 144–152.
  • [4] W.E. Hoggat, Jr: Fibonacci and Lucas numbers. A publication of The Fibonacci Association, University of Santa Clara, CA 95053.
  • [5] D. Jarden: “Nullifying coefficiens”, Scripta Math., Vol. 19, (1953), pp. 239–241.
  • [6] E. Krot: “ψ-extensions of q-Hermite and q-Laguerre Polynomials-properties and principal statements”, Czech. J. Phys., Vol. 51 (12), (2001), pp. 1362–1367. http://dx.doi.org/10.1023/A:1013382322526
  • [7] A.K. Kwaśniewski: “Towards ψ-Extension of Rota's Finite Operator Calculus”, Rep. Math. Phys., Vol. 47(305), (2001), pp. 305–342. http://dx.doi.org/10.1016/S0034-4877(01)80092-6
  • [8] G. Markowsky: “Differential operators and the Theory of Binomial Enumeration”, Math. Anal. Appl., Vol. 63 (145), (1978).
  • [9] S. Pincherle and U. Amaldi: Le operazioni distributive e le loro applicazioni all analisi, N. Zanichelli, Bologna, 1901.
  • [10] G.-C. Rota: Finite Operator Calculus, Academic Press, New York, 1975.
  • [11] G.C. Rota and R. Mullin: “On the Foundations of cCombinatorial Theory, III: Theory of binominal Enumeration”, In: Graph Theory and its Applications, Academic Press, New York, 1970.
  • [12] http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Fibonacci.html
  • [13] A.K. Kwaśniewski: “Information on Some Recent Applications of Umbral Extensions to Discrete Mathematics”, ArXiv:math.CO/0411145, Vol. 7, (2004), to be presented at ISRAMA Congress, Calcuta-India, December 2004
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475975
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