On a generalization of duality triads

• Autorzy: Matthias Schork
• Języki publikacji: EN

Abstrakty

EN

Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.

Słowa kluczowe

EN

Duality triad; recurrence relation; inversion relation; 05Axx; 11B37; 11B83

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 2
• Strony: 304-318

Daty

wydano

2006-06-01

online

2006-06-01

Twórcy

autor

Matthias Schork

Bibliografia

• [1] G.E. Andrews: The Theory of Partitions, Addison Wesley, Reading, 1976.
• [2] G. Bach: “Über eine Verallgemeinerung der Differenzengleichung der Stirlingschen Zahlen 2.Art und einige damit zusammenhängende Fragen”, J. Reine Angew. Math., Vol. 233, (1968), pp. 213–220.
• [3] P. Blasiak, K.A. Penson and A.I. Solomon: “The Boson Normal Ordering Problem and Generalized Bell Numbers”, Ann. Comb., Vol. 7, (2003), pp. 127–139. http://dx.doi.org/10.1007/s00026-003-0177-z
• [4] E. Borak: “A note on special duality triads and their operator valued counterparts”, Preprint: arXiv:math.CO/0411041.
• [5] L. Comtet: Advanced Combinatorics, Reidel, Dordrecht, 1974.
• [6] L. Comtet: “Nombres de Stirling généraux et fonctions symétriques,” C. R. Acad. Sc. Paris, Vol. 275, (1972), pp. 747–750.
• [7] P. Feinsilver and R. Schott: Algebraic structures and operator calculus. Vol. II: Special functions and computer science, Kluwer Academic Publishers, Dordrecht, 1994.
• [8] I. Jaroszewski and A.K. Kwásniewski: “On the principal recurrence of data structures organization and orthogonal polynomials”, Integral Transforms Spec. Funct., Vol. 11, (2001), pp. 1–12.
• [9] J. Konvalina: “Generalized binomial coefficients and the subset-subspace problem”, Adv. Math., Vol. 21, (1998), pp. 228–240.
• [10] J. Konvalina: “A unified interpretation of the Binomial Coefficients, the Stirling Numbers and Gaussian Coefficents,” Amer. Math. Monthly, Vol. 107, (2000), pp. 901–910.
• [11] A.K. Kwaśniewski: “On duality triads,” Bull. Soc. Sci. Lettres Łódź, Vol. A 53, Ser. Rech. Déform. 42, (2003), pp. 11–25.
• [12] A.K. Kwaśniewski: “On Fibonomial and other triangles versus duality triads”, Bull. Soc. Sci. Lettres Łódź, Vol. A 53, Ser. Rech. Déform. 42, (2003), pp. 27–37.
• [13] A.K. Kwaśniewski: “Fibonomial Cumulative Connection Constants”, Bulletin of the ICA, Vol. 44, (2005), pp. 81–92.
• [14] M. Schork: “Some remarks on duality triads”, Adv. Stud. Contemp. Math., to appear.
• [15] R.P. Stanley: Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999.
• [16] B. Voigt: “A common generalization of binomial coefficients, Stirling numbers and Gaussian coefficents”, Publ. I.R.M.A. Strasbourg, Actes 8 e Séminaire Lotharingien, Vol. 229/S-08, (1984), pp. 87–89.
• [17] W. Woan: “A Recursive Relation for Weighted Motzkin Sequences”, J. Integer Seq., Vol. 8, (2005), art. 05.1.6.
• [18] S. Wolfram: A new kind of science, Wolfram Media, Champaign, 2002.

Identyfikatory

DOI

10.2478/s11533-006-0008-7