Abstract
This research presents the reader some algebraic operations related to combinatorial games and gives a detailed outlook of a special game called Hackenbush game. We will deduce a group with a special feature with the help of some basic algebraic concepts. A fresh outlook to some combinatorial mathematical algebraic operations and concepts through the evaluation of a deduced group from this game.
Highlights
As a result of the many mathematical research done by Lagrange, Abel, Galois, and others in the fields of geometry, number’s theory, and algebraic equations at the end of the eighteenth century, early nineteenth century, the mathematical theory of “groups” was discovered [1,2,3]
By analyzing the structures of graphs, we can deduce the properties of their related groups, which can be done by exploiting the notion of “identity” in “group theory.”
What happens if we considered the multiplication’s operation on what we have analyzed above
Summary
As a result of the many mathematical research done by Lagrange, Abel, Galois, and others in the fields of geometry, number’s theory, and algebraic equations at the end of the eighteenth century, early nineteenth century, the mathematical theory of “groups” was discovered [1,2,3]. We will utilize the concepts of “graph theory” to analyze some combinatorial mathematical algebraic operations and concepts through the evaluation of a deduced group from a combinatorial game called “Hackenbush game.” The game is defined with the following attributes: (A) There are two players, left and right.
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