  We study heaps of pieces for lattice paths, which give a combinatorial
visualization of lattice paths. We introduce two types of heaps: type $I$ and
type $II$. A heap of type $I$ is characterized by peaks of a lattice path. We
have a duality between a lattice path $\mu$ and its dual $\overline{\mu}$ on
heaps of type $I$. A heap of type $II$ for $\mu$ is characterized by the skew
shape between the lowest path and $\mu$. We give a determinant expression for
the generating function of heaps for general lattice paths, and an explicit
formula for rational $(1,k)$-Dyck paths by using the inversion lemma. We
introduce and study heaps in $k+1$-dimensions which are bijective to heaps of
type $II$ for $(1,k)$-Dyck paths. Further, we show a bijective correspondence
between type $I$ and type $II$ in the case of rational $(1,k)$-Dyck paths. As
another application of heaps, we give two explicit formulae for the generating
function of heaps for symmetric Dyck paths in terms of statistics on Dyck paths
and on symmetric Dyck paths respectively.
