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On a class of skew Dyck paths | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 1، دوره 10، شماره 4، اسفند 2025، صفحه 305-319 اصل مقاله (305.25 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.12170.1141 | ||
| نویسندگان | ||
| Yvonne Wakuthii Kariuki1؛ Isaac Owino Okoth* 2 | ||
| 1Department of Mathematics, Kibabii University, Bungoma, Kenya. | ||
| 2Department of Pure and Applied Mathematics, School of Mathematics, Statistics and Actuarial Science, Maseno University, Maseno, Kenya | ||
| تاریخ دریافت: 31 خرداد 1404، تاریخ بازنگری: 19 شهریور 1404، تاریخ پذیرش: 06 آذر 1404 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| box؛ bijection؛ binary؛ log-convex؛ plane tree | ||
| مراجع | ||
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