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2006 | 4 | 3 | 507-524
Tytuł artykułu

Duality triads of higher rank: Further properties and some examples

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
3
Strony
507-524
Opis fizyczny
Daty
wydano
2006-09-01
online
2006-09-01
Bibliografia
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  • [2] 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
  • [3] P. Blasiak, K.A. Penson and A.I. Solomon: “The general boson normal ordering problem”, Phys. Lett. A, Vol. 309, (2003), pp. 198–205. http://dx.doi.org/10.1016/S0375-9601(03)00194-4
  • [4] E. Borak: “A note on special duality triads and their operator valued counterparts”, Preprint arXiv:math.CO/0411041.
  • [5] T.S. Chihara: An Introduction to Orthogonal Polynomials, Gordon & Breach, New York, 1978.
  • [6] L. Comtet: Advanced Combinatorics, Reidel, Dordrecht, 1974.
  • [7] A.J. Duran and W. Van Assche: “Orthogonal matrix polynomials and higher order recurrence relations”, Linear Algebra Appl., Vol. 219, (1995), pp. 261–280. http://dx.doi.org/10.1016/0024-3795(93)00218-O
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  • [9] I. Jaroszewski and A.K. Kwaśniewski: “On the principal recurrence of data structures organization and orthogonal polynomials”, Integral Transforms Spec. Funct., Vol. 11, (2001), pp. 1–12.
  • [10] A.K. Kwaśniewski: “On duality triads”, Bull. Soc. Sci. Lettres Łódź, Vol. A 53, Ser. Rech. Déform. 42 (2003), pp. 11–25.
  • [11] 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.
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  • [13] A.K. Kwaśniewski: “On umbral extensions of Stirling numbers and Dobinski-like formulas”, Adv. Stud. Contemp. Math., Vol. 12, (2006), pp. 73–100.
  • [14] F. Marcellán and A. Ronveaux: “On a class of polynomials orthogonal with respect to a discrete Sobolev inner product”, Indag. Math., Vol. 1, (1990), pp. 451–464. http://dx.doi.org/10.1016/0019-3577(90)90013-D
  • [15] F. Marcellán and G. Sansigre: “On a Class of Matrix Orthogonal Polynomials on the Real Line”, Linear Algebra Appl., Vol. 181, (1993), pp. 97–109. http://dx.doi.org/10.1016/0024-3795(93)90026-K
  • [16] J. Riordan: Combinatorial Identities, Wiley, New York, 1968.
  • [17] M. Schork: “On the combinatorics of normal-ordering bosonic operators and deformations of it”, J. Phys. A: Math. Gen., Vol. 36, (2003), pp. 4651–4665. http://dx.doi.org/10.1088/0305-4470/36/16/314
  • [18] M. Schork: “Some remarks on duality triads”, Adv. Stud. Contemp. Math., Vol. 12, (2006), pp. 101–110.
  • [19] M. Schork: “On a generalization of duality triads”, Cent. Eur. J. Math., Vol. 4(2), (2006), pp. 304–318. http://dx.doi.org/10.2478/s11533-006-0008-7
  • [20] A. Sinap and W. Van Assche: “Orthogonal matrix polynomials and applications”, J. Comput. Appl. Math., Vol. 66, (1996), pp. 27–52. http://dx.doi.org/10.1016/0377-0427(95)00193-X
  • [21] R.P. Stanley: Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999.
  • [22] G. Szegö: Orthogonal Polynomials, American Mathematical Society, 1948.
  • [23] V. Totik: “Orthogonal Polynomials”, Surv. Approximation Theory, Vol. 1, (2005), pp. 70–125.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-006-0015-8
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