On multi F-nomial coefficients and Inversion formula for F-nomial coefficients
Combinatorics
2009-09-29 v2 Discrete Mathematics
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.
Cite
@article{arxiv.0806.3626,
title = {On multi F-nomial coefficients and Inversion formula for F-nomial coefficients},
author = {M. Dziemianczuk},
journal= {arXiv preprint arXiv:0806.3626},
year = {2009}
}
Comments
11 pages, 2 figures