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September 12, 2025Mathematics0 citationsOpen Access

Promotion of Lattice Paths Using Riordan Arrays and Transformations

Promotion of Lattice Paths by Riordan Arrays

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Authors

AHAoife HennessyWaterford Institute of TechnologyKMKieran MurphyAgriculture VictoriaNGNarciso GonzagaWaterford Institute of Technology

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Overview

This paper demonstrates how riordan arrays promote dyck paths to motzkin and schröder paths, highlighting new combinatorial insights.

Key Points

  • Promoting dyck paths to generalized motzkin and schröder paths reveals hidden integer sequences.
  • The binomial and chebyshev transforms map dyck paths using riordan arrays, establishing key transformations.
  • The framework includes an analysis of grand paths that cross below the x-axis, extending classic lattice path studies.
  • Bijective correspondences between promoted path families bring novel understanding to known combinatorial structures.
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Cite This Study

Hennessy et al. (2025) studied this question.

synapsesocial.com/papers/68d44a4031b076d99fa537bahttps://doi.org/10.3390/math13182949
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