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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, 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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