Periodicity and Other Structure in a Colorful Family of Nim-like Arrays
نویسندگان
چکیده
We study aspects of the combinatorial and graphical structure shared by a certain family of recursively generated arrays related to the operation of Nimaddition. In particular, these arrays display periodic behavior along rows and diagonals. We explain how various features of computer-generated graphics depicting these arrays are reflections of the theorems we prove.
منابع مشابه
Algebraic Structure in a Family of Nim-like Arrays
We study aspects of the algebraic structure shared by a certain family of recursively generated arrays related to the operation of Nim-addition. We first observe that each individual array represents a countably infinite, commutative loop (in the sense of quasigroups). We then prove that each loop in the family is monogenic (generated by a single element in a non-associative fashion), and use t...
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عنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010