Counting asymmetric weighted pyramids in non-decreasing Dyck paths

A Dyck path is non-decreasing if the y-coordinates of its valleys form a non-decreasing sequence. A pyramid is asymmetric if the valleys determining the maximal pyramid are at distinct levels. In this paper we count non-decreasing Dyck paths having asymmetric pyramids of a fixed height at a fixed level in the path. These paths are counted using generating functions (by the symbolic method) and recurrence relations. We parameterize the results found here using Riordan arrays. We have found some relations between the asymmetric pyramids with the p-ascent sequences, the asymmetric Delannoy paths, the q-Catalan numbers, and the Fibonacci polynomials. ISSN: 2202-3518 c ©The author(s). Released under the CC BY 4.0 International License R. FLÓREZ ET AL. /AUSTRALAS. J. COMBIN. 79 (1) (2021), 123–140 124

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