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

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

On a class of skew Dyck paths

Keywords

Main Subjects


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Volume 10, Issue 4
December 2025
Pages 305-319
  • Receive Date: 21 June 2025
  • Revise Date: 10 September 2025
  • Accept Date: 27 November 2025
  • First Publish Date: 28 November 2025
  • Publish Date: 01 December 2025