An introduction to finite fibonomial calculus

Ewa Krot

Open Mathematics (2004)

  • Volume: 2, Issue: 5, page 754-766
  • ISSN: 2391-5455

Abstract

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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].

How to cite

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Ewa Krot. "An introduction to finite fibonomial calculus." Open Mathematics 2.5 (2004): 754-766. <http://eudml.org/doc/268756>.

@article{EwaKrot2004,
abstract = {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].},
author = {Ewa Krot},
journal = {Open Mathematics},
keywords = {11C08; 11B37; 47B47},
language = {eng},
number = {5},
pages = {754-766},
title = {An introduction to finite fibonomial calculus},
url = {http://eudml.org/doc/268756},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Ewa Krot
TI - An introduction to finite fibonomial calculus
JO - Open Mathematics
PY - 2004
VL - 2
IS - 5
SP - 754
EP - 766
AB - 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].
LA - eng
KW - 11C08; 11B37; 47B47
UR - http://eudml.org/doc/268756
ER -

References

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  1. [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. [2] R.L. Graham, D.E. Knuth and O. Patashnik: Concrete mathematics. A Foundation for Computer Science, Addison-Wesley Publishing Company, Inc., Massachusetts, 1994. Zbl0836.00001
  3. [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. [4] W.E. Hoggat, Jr: Fibonacci and Lucas numbers. A publication of The Fibonacci Association, University of Santa Clara, CA 95053. 
  5. [5] D. Jarden: “Nullifying coefficiens”, Scripta Math., Vol. 19, (1953), pp. 239–241. 
  6. [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 Zbl1057.33013
  7. [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 Zbl0994.05019
  8. [8] G. Markowsky: “Differential operators and the Theory of Binomial Enumeration”, Math. Anal. Appl., Vol. 63 (145), (1978). Zbl0376.05002
  9. [9] S. Pincherle and U. Amaldi: Le operazioni distributive e le loro applicazioni all analisi, N. Zanichelli, Bologna, 1901. 
  10. [10] G.-C. Rota: Finite Operator Calculus, Academic Press, New York, 1975. 
  11. [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. [12] http://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Fibonacci.html 
  13. [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 Zbl1087.05010

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