On a generalization of duality triads

Matthias Schork

Open Mathematics (2006)

  • Volume: 4, Issue: 2, page 304-318
  • ISSN: 2391-5455

Abstract

top
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.

How to cite

top

Matthias Schork. "On a generalization of duality triads." Open Mathematics 4.2 (2006): 304-318. <http://eudml.org/doc/269718>.

@article{MatthiasSchork2006,
abstract = {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.},
author = {Matthias Schork},
journal = {Open Mathematics},
keywords = {05Axx; 11B37; 11B83},
language = {eng},
number = {2},
pages = {304-318},
title = {On a generalization of duality triads},
url = {http://eudml.org/doc/269718},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Matthias Schork
TI - On a generalization of duality triads
JO - Open Mathematics
PY - 2006
VL - 4
IS - 2
SP - 304
EP - 318
AB - 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.
LA - eng
KW - 05Axx; 11B37; 11B83
UR - http://eudml.org/doc/269718
ER -

References

top
  1. [1] G.E. Andrews: The Theory of Partitions, Addison Wesley, Reading, 1976. 
  2. [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. Zbl0169.31902
  3. [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 Zbl1030.81004
  4. [4] E. Borak: “A note on special duality triads and their operator valued counterparts”, Preprint: arXiv:math.CO/0411041. 
  5. [5] L. Comtet: Advanced Combinatorics, Reidel, Dordrecht, 1974. 
  6. [6] L. Comtet: “Nombres de Stirling généraux et fonctions symétriques,” C. R. Acad. Sc. Paris, Vol. 275, (1972), pp. 747–750. Zbl0246.05006
  7. [7] P. Feinsilver and R. Schott: Algebraic structures and operator calculus. Vol. II: Special functions and computer science, Kluwer Academic Publishers, Dordrecht, 1994. Zbl1128.33300
  8. [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. Zbl0982.68049
  9. [9] J. Konvalina: “Generalized binomial coefficients and the subset-subspace problem”, Adv. Math., Vol. 21, (1998), pp. 228–240. Zbl0936.05003
  10. [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. Zbl0987.05004
  11. [11] A.K. Kwaśniewski: “On duality triads,” Bull. Soc. Sci. Lettres Łódź, Vol. A 53, Ser. Rech. Déform. 42, (2003), pp. 11–25. Zbl1152.11306
  12. [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. Zbl1152.11307
  13. [13] A.K. Kwaśniewski: “Fibonomial Cumulative Connection Constants”, Bulletin of the ICA, Vol. 44, (2005), pp. 81–92. Zbl1075.11010
  14. [14] M. Schork: “Some remarks on duality triads”, Adv. Stud. Contemp. Math., to appear. Zbl1102.11010
  15. [15] R.P. Stanley: Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999. Zbl0928.05001
  16. [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. [17] W. Woan: “A Recursive Relation for Weighted Motzkin Sequences”, J. Integer Seq., Vol. 8, (2005), art. 05.1.6. Zbl1065.05012
  18. [18] S. Wolfram: A new kind of science, Wolfram Media, Champaign, 2002. Zbl1022.68084

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.