  We find a bijection between bi-banded paths and peak-counting paths, applying
to two classes of lattice paths including Dyck paths. Thus we find a new
interpretation of Narayana numbers as coefficients of weight polynomials
enumerating bi-banded Dyck paths, which class of paths has arisen naturally in
previous literature in a solution of the stationary state of the `TASEP'
stochastic process.
