Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Rothe numbers (aka generalized Catalan numbers) have a natural interpretation in terms of lattice paths. Making use of this interpretation this paper aims at showing how some classical convolution identities involving Rothe numbers can also be proved conveniently using lattice path combinatorics.
Wydawca
Czasopismo
Rocznik
Tom
Strony
265--277
Opis fizyczny
Bibliogr. 12 poz., wykr.
Twórcy
autor
- Applied Computer Science Department of Information Systems and Operations Vienna University of Economics and Business, Austria, wolfgang.panny@wu.ac.at
Bibliografia
- [1] Dershowitz, N., Zaks, S.: The cycle lemma and some applications, European Journal of Combinatorics, 11, 1990, 35-40.
- [2] Dvoretzky, A., Motzkin, T.: A problem of arrangements, Duke Mathematical Journal, 14(2), 1947, 305-313.
- [3] Gould, H. W.: Some generalizations of Vandermonde's convolution, The American Mathematical Monthly, 63(2), 1956, 84-91.
- [4] Gould, H. W.: Combinatorial Identities, http://www.math.wvu.edu/~gould/Vol5.PDF.
- [5] Gould, H. W., Kauck´y, J.: Evaluation of a class of binomial coefficient summations, Journal of Combinatorial History, 1(2), 1966, 233-247.
- [6] Grossman, H. D.: Fun with lattice points-21, Scripta Mathematica, 16, 1950, 120-124.
- [7] Hagen, J. G.: Synopsis der höheren Mathematik, Erster Band: Arithmetische und algebraische Analyse, Verlag von Felix L. Dames, Berlin, 1891.
- [8] Hofbauer, J.: Lagrange-Inversion, Actes du Séminaire Lotharingien du Combinatoire, 6, 1982.
- [9] Mohanty, S. G.: Lattice Path Counting and Applications, Academic Press, New York, 1979.
- [10] Richardson Jr., S. L.: Enumeration of the generalized Catalan numbers, Thesis submitted to the Eberly College of Arts and Sciences at West Virginia University,Morgantown, 2005.
- [11] Rothe, H. A.: Formulae de serierum reversione demonstratio universalis signis localibus combinatorioanalyticorum vicariis exhibita, Leipzig, 1793.
- [12] Smiley, L.: Hagen's identity from Catalanian forests (preprint), http://www.math.uaa.alaska.edu/~smiley/question4Dave.pdf, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0026-0016