On a generalization of duality triads
Matthias Schork
Open Mathematics, Tome 4 (2006), p. 304-318 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:269718 
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     pages = {304-318},
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Matthias Schork. On a generalization of duality triads. Open Mathematics, Tome 4 (2006) pp. 304-318. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0008-7/

[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. | Zbl 0169.31902

[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 | Zbl 1030.81004

[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. | Zbl 0246.05006

[7] P. Feinsilver and R. Schott: Algebraic structures and operator calculus. Vol. II: Special functions and computer science, Kluwer Academic Publishers, Dordrecht, 1994. | Zbl 1128.33300

[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. | Zbl 0982.68049

[9] J. Konvalina: “Generalized binomial coefficients and the subset-subspace problem”, Adv. Math., Vol. 21, (1998), pp. 228–240. | Zbl 0936.05003

[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. | Zbl 0987.05004

[11] A.K. Kwaśniewski: “On duality triads,” Bull. Soc. Sci. Lettres Łódź, Vol. A 53, Ser. Rech. Déform. 42, (2003), pp. 11–25. | Zbl 1152.11306

[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. | Zbl 1152.11307

[13] A.K. Kwaśniewski: “Fibonomial Cumulative Connection Constants”, Bulletin of the ICA, Vol. 44, (2005), pp. 81–92. | Zbl 1075.11010

[14] M. Schork: “Some remarks on duality triads”, Adv. Stud. Contemp. Math., to appear. | Zbl 1102.11010

[15] R.P. Stanley: Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999. | Zbl 0928.05001

[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. | Zbl 1065.05012

[18] S. Wolfram: A new kind of science, Wolfram Media, Champaign, 2002. | Zbl 1022.68084