  Multimodular functions, primarily used in the literature of queueing theory,
discrete-event systems, and operations research, constitute a fundamental
function class in discrete convex analysis. The objective of this paper is to
clarify the properties of multimodular functions with respect to fundamental
operations such as permutation and scaling of variables, projection (partial
minimization) and convolution. It is shown, in particular, that the class of
multimodular functions is stable under projection under a certain natural
condition on the variables to be minimized, and the convolution of two
multimodular functions is not necessarily multimodular, even in the special
case of the convolution of a multimodular function with a separable convex
function.
