Some Enumerations on Non-Decreasing Dyck Paths

  • Éva Czabarka
  • Rigoberto Flórez
  • Leandro Junes
Keywords: Generating functions, Non-decreasing Dyck paths, Path weight, valley, pyramid, Fibonacci Numbers,


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.
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