Some simple bijections involving lattice walks and ballot sequences

Details Some simple bijections involving lattice walks and ballot sequences Some simple bijections involving lattice walks and ballot sequences

2010-10-23

arxiv.org/abs/1010.4847v1

Mathematics

Combinatorics

Scientific paper

In this note we observe that a bijection related to Littelmann's root operators (for type $A_1$) transparently explains the well known enumeration by length of walks on $\N$ (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.

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