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

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_{k_1,k_2,...,k_s} of layer <Phi_1-->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.

11 pages, 2 figures

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Cited by in corpus (8)

• Cobweb posets - Recent Results
• On Cobweb Posets and Discrete F-Boxes Tilings
• Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients
• Graded posets inverse zeta matrix formula
• Generalization of Fibonomial Coefficients
• Natural join construction of graded posets versus ordinal sum and discrete hyper boxes
• On natural join of posets properties and first applications
• Note on Ward-Horadam H(x) - binomials' recurrences and related interpretations, II