Bi-banded paths, a bijection and the Narayana numbers

Abstract

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. Show more