# An introduction to finite fibonomial calculus

Open Mathematics (2004)

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

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topEwa 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

top- [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. Zbl0836.00001
- [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 Zbl1057.33013
- [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] G. Markowsky: “Differential operators and the Theory of Binomial Enumeration”, Math. Anal. Appl., Vol. 63 (145), (1978). Zbl0376.05002
- [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 Zbl1087.05010

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