Gray visiting Motzkins

Abstract.

We present the first Gray code for Motzkin words and their generalizations: k colored Motzkin words and Schröder words. The construction of these Gray codes is based on the observation that a k colored Motzkin word is the shuffle of a Dyck word by a k-ary variation on a trajectory which is a combination. In the final part of the paper we give some algorithmic considerations and other possible applications of the techniques introduced here.