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2006 | 4 | 2 | 304-318
Tytuł artykułu

On a generalization of duality triads

Autorzy
Treść / Zawartość
Warianty tytułu
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
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
2
Strony
304-318
Opis fizyczny
Daty
wydano
2006-06-01
online
2006-06-01
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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0008-7
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