Some bijections for lattice paths

Abstract

We present three bijections, the first between little Schr\"{o}der paths and a class of growth-constrained integer sequences, the second between lattice paths consisting of steps with nonnegative slope and another class of growth-constrained sequences, the third between a class of lattice paths with steps $(1,1)$ and $(1,-j\,),\ j\ge 1$, and a class with steps $(k,1),\ k\ge 1$, and $(1,-1)$.