Some Enumerations on Non-Decreasing Dyck Paths

Éva Czabarka, Rigoberto Flórez, Leandro Junes

Abstract


We construct a formal power series on several variables that encodes many statistics on non-decreasing Dyck paths. In particular, we use this formal power series to count peaks, pyramid weights, and indexed sums of pyramid weights for all non-decreasing Dyck paths of length $2n.$ We also show that an indexed sum on pyramid weights depends only on the size and maximum element of the indexing set.

Keywords


Generating functions; Non-decreasing Dyck paths; Path weight; valley; pyramid; Fibonacci Numbers;

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