  Extensive studies of Boolean functions are carried in many fields. The Mobius
transform is often involved for these studies. In particular, it plays a
central role in coincident functions, the class of Boolean functions invariant
by this transformation. This class -- which has been recently introduced -- has
interesting properties, in particular if we want to control both the Hamming
weight and the degree. We propose an innovative way to handle the Mobius
transform which allows the composition between several Boolean functions and
the use of Shannon or Reed-Muller decompositions. Thus we benefit from a better
knowledge of coin-cident functions and introduce new properties. We show
experimentally that for many features, coincident functions look like any
Boolean functions.
