Several Remarks on q-Binomial Inverse Formula and Examples

摘要

In this paper, we first give some comments on the paper [J. Goldman and G. C. Rota, on the foundations of combinatorial theory IV finite vector spaces and Eulerian generating functions, Stud. Appl. Math., 49: 239--258 (1970)]. In that paper, Goldman and Rota showed two incorrect inversion formulas in Section 3. We point out the formulas and give the correct versions with the proof in this this paper first. Then we give some remarks on q -binomial inverse formula concerning its applications.