Some simple bijections involving lattice walks and ballot sequences
arXiv:1010.4847
Abstract
In this note we observe that a bijection related to Littelmann's root operators (for type ) transparently explains the well known enumeration by length of walks on (left factors of Dyck paths), as well as some other enumerative coincidences. We indicate a relation with bijective solutions of Bertrand's ballot problem: those can be mechanically transformed into bijective proofs of the mentioned enumeration formula.