Abstract :
In the game of chess, the knight’s moves have a shape of L. We will present enumeration of certain knight’s paths in the plane, called zigzag knight’s paths, under some constraints (ending at ordinate 0, bounded by a horizontal line…). We present our results in form
of generating functions or direct closed-form expressions. We derive asymptotic results, finding approximations for quantities such as the probability that a knight’s path stays in some area of the plane, or for the average ordinate of such a path. Additionally, certain counting sequences that we will encounter already count known objects, we will provide bijections between knight’s paths and those objects.
Bio :
Nathanaël est en 1ère année de thèse au LIB dans l’équipe CombiNet sous la direction de Jean-Luc Baril, Vincent Vajnovszki et Sergey Kirgizov. Nathanaël travaille sur des sujets variés de combinatoire.