An introduction to finite fibonomial calculus

• Autorzy: Ewa Krot
• Języki publikacji: 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].

Słowa kluczowe

EN

Fibonacci numbers; Fibonomial Calculus; Sheffer F-polynomials; 11C08; 11B37; 47B47

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 5
• Strony: 754-766

Daty

wydano

2004-10-01

online

2004-10-01

Twórcy

autor

Ewa Krot

• Białystok University

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

Identyfikatory

DOI

10.2478/BF02475975