On multi F-nomial coefficients and Inversion formula for F-nomial coefficients

2008/06/23 by Maciej Dziemiańczuk, M. Dziemianczuk, Dziemianczuk, M.
Computer Science · Mathematics · #05A19 #11B39 #15A09 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Data Management and Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO #msc:05A19 #msc:11B39 #msc:15A09 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0806.3626

11 pages, 2 figures

openalex publication_date 2008/06/23 · arxiv created 2008/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In response to [6], we discover the looked for inversion formula for F-nomial coefficients. Before supplying its proof, we generalize F-nomial coefficients to multi F-nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form sP_k1,k2,...,ks of layer Phi_n>. Then we present inversion formula for F-nomial coefficients using multi F-nomial coefficients for all cobweb-admissible sequences. To this end we infer also some identities as conclusions of that inversion formula for the case of binomial, Gaussian and Fibonomial coefficients.

Citations

• On incidence algebras description of cobweb posets
• Reduced Incidence algebras description of cobweb posets and KoDAGs
• An introduction to finite fibonomial calculus

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