2009/08/22 by Maciej Dziemiańczuk, M. Dziemianczuk, Dziemianczuk, M. · 1 citation
Mathematics · Physics and Astronomy · #05A10 #11B39 #11B65 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #math.CO #msc:05A10 #msc:11B39 #msc:11B65
paper · pdf · doi:10.48550/arxiv.0908.3248
13 pages, The Internet Gian-Carlo Rota Polish Seminar article, No 9, Subject 5, http://ii.uwb.edu.pl/akk/sem/sem_rota.htm
arxiv created 2009/08/22 · openalex publication_date 2009/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.