On a class of skew Dyck paths

Kariuki, Yvonne Wakuthii; Okoth, Isaac Owino

doi:10.22061/jdma.2025.12170.1141

On a class of skew Dyck paths

Document Type : Full Length Article

Authors

¹ Department of Mathematics, Kibabii University, Bungoma, Kenya.

² Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya

10.22061/jdma.2025.12170.1141

Abstract

This paper introduces the set of skew 2-Dyck paths- Dyck-like lattice paths that allow unit up-steps, down-steps of length 2, and left-steps of length 2, provided the paths remain non intersecting. An explicit enumeration formula for these paths is derived using the symbolic method and the Lagrange Inversion Formula. In addition, the paper defines three related combinatorial structures: 2-labeled box paths, 3-leaf-labeled plane trees, and 2-edge-labeled plane trees. Bijections are constructed between the set of skew 2-Dyck paths and the set of each of these three structures, thereby demonstrating their enumerative equivalence.

Graphical Abstract