  The authors have proved in [J. Algebra Appl. 14 (2015), no. 6] that the size
of a stratifying system over a finite-dimensional hereditary path algebra $A$
is at most $n$, where $n$ is the number of isomorphism classes of simple
$A$-modules. Moreover, if $A$ is of Euclidean type a stratifying system over
$A$ has at most $n-2$ regular modules. In this work, we construct a family of
stratifying systems of size $n$ with a maximal number of regular elements, over
the hereditary path algebra with quiver $\widetilde{\mathbb {A}}_{p,q} $,
canonically oriented.
