MEANDRIC NUMBER Meaning and
Definition
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A meandric number is a mathematical concept defined as a positive integer that represents the number of closed meanders that can be formed on a plane. A closed meander is a self-avoiding closed curve on a grid, consisting of horizontal and vertical line segments. It is notable that no two segments of the meander can cross or touch each other, and the beginning and endpoint of the curve must coincide. Additionally, the curve cannot visit any position more than once, excluding the starting and ending point.
The term "meandric" originates from the Latin word "meander," which refers to a winding or convoluted path. The concept of meandric numbers arises from combinatorial mathematics and specifically focuses on the enumeration and counting of various types of curves that satisfy certain constraints.
Meandric numbers have applications in fields such as topology, graph theory, and statistical physics. They provide a unique way to classify and analyze self-avoiding curves and their properties. Meandric numbers can be computed through various methods, including the use of generating functions and recursive formulas. By studying meandric numbers, mathematicians gain insight into the complexity and behavior of self-avoiding curves, leading to advancements in diverse scientific disciplines.
