Generalization of Fibonomial Coefficients

Details Generalization of Fibonomial Coefficients Generalization of Fibonomial Coefficients

2009-08-22

arxiv.org/abs/0908.3248v1

Mathematics

Combinatorics

13 pages, The Internet Gian-Carlo Rota Polish Seminar article, No 9, Subject 5, http://ii.uwb.edu.pl/akk/sem/sem_rota.htm

Scientific paper

Following Lucas and then other Fibonacci people Kwasniewski had introduced and had started ten years ago the open investigation of the overall F-nomial coefficients which encompass among others Binomial, Gaussian and Fibonomial coefficients with a new unified combinatorial interpretation expressed in terms of cobweb posets' partitions and tilings of discrete hyperboxes. In this paper, we deal with special subfamily of T-nomial coefficients. The main aim of this note is to develop the theory of T-nomial coefficients with the help of generating functions. The binomial-like theorem for T-nomials is delivered here and some consequences of it are drawn. A new combinatorial interpretation of T-nomial coefficients is provided and compared with the Konvalina way of objects' selections from weighted boxes. A brief summary of already known properties of T-nomial coefficients is served.

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