On a generalized convolution of incidence functions (Q1974524)

The author defines a class of convolutions (called by him \(K\)-convolutions) on the set of incidence functions defined on a locally finite partially order set. This generalizes the \(K\)-convolutions on the set of arithmetical functions [see e.g. \textit{P. J. McCarthy}, Introduction to arithmetical functions, Springer, New York (1986; Zbl 0591.10003)]. It is shown that certain results of \textit{L. Carlitz} and \textit{M. V. Subbarao} [Duke Math. J. 40, 949-958 (1973; Zbl 0277.10007)] and the author [Can. Math. Bull. 32, 467-473 (1989; Zbl 0681.10002)] can be generalized to this abstract setting.