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

References in corpus (4)

• On Cobweb posets tiling problem
• On incidence algebras description of cobweb posets
• On Cobweb Posets and Discrete F-Boxes Tilings
• Reduced Incidence algebras description of cobweb posets and KoDAGs

Cited by in corpus (5)

• On Cobweb Posets and Discrete F-Boxes Tilings
• Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients
• Generalization of Fibonomial Coefficients
• On natural join of posets properties and first applications
• Natural join construction of graded posets versus ordinal sum and discrete hyper boxes