Report
Grand zigzag knight's paths
| العنوان: | Grand zigzag knight's paths |
|---|---|
| المؤلفون: | Baril, Jean-Luc, Hassler, Nathanaël, Kirgizov, Sergey, Ramírez, José L. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Computer Science - Discrete Mathematics |
| الوصف: | We study the enumeration of different classes of grand knight's paths in the plane. In particular, we focus on the subsets of zigzag knight's paths that are subject to constraints. These constraints include ending at $y$-coordinate 0, bounded by a horizontal line, confined within a tube, among other considerations. We present our results using generating functions or direct closed-form expressions. We derive asymptotic results, finding approximations for quantities such as the probability that a zigzag knight's path stays in some area of the plane, or for the average of the altitude of such a path. Additionally, we exhibit some bijections between grand zigzag knight's paths and some pairs of compositions. Comment: 17 pages, 9 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.04851 |
| رقم الانضمام: | edsarx.2402.04851 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |