  We propose an original approach to the problem of rankunimodality for Dyck
lattices. It is based on a well known recursive construction of Dyck paths
originally developed in the context of the ECO methodology, which provides a
partition of Dyck lattices into saturated chains. Even if we are not able to
prove that Dyck lattices are rank-unimodal, we describe a family of polynomials
(which constitutes a polynomial analog of ballot numbers) and a succession rule
which appear to be useful in addressing such a problem. At the end of the
paper, we also propose and begin a systematic investigation of the problem of
unimodality of succession rules.
