  Absolutely superficial sequences was introduced by P. Schenzel in order to
study generalized Cohen-Macaulay (resp. Buchsbaum) modules. For an arbitrary
local ring, they turned out to be d-sequences. This paper established
properties of absolutely superficial sequences with respect to a module. It is
shown that they are closely related to other sequences in the theory of
generalized Cohen-Macaulay (resp. Buchsbaum) modules. In particular, there is a
bounding function for the Hilbert-Samuel function of every parameter ideal such
that this bounding function is attained if and only if the ideal is generated
by an absolutely superficial sequence.
