  For two differentiable maps between two manifolds of possibly different
dimensions, the local and global coincidence homology classes are introduced
and studied by Bisi- Bracci-Izawa-Suwa (2016) in the framework of Cech-de Rham
cohomology. We take up the problem from the combinatorial viewpoint and give
some finer results, in particular for the local classes. As to the global
class, we clarify the relation with the cohomology coincidence class as studied
by Biasi-Libardi-Monis (2015). In fact they introduced such a class in the
context of several maps and we also consider this case. In particular we define
the local homology class and give some explicit expressions. These all together
lead to a generalization of the classical Lefschetz coincidence point formula.
