运用数学实验解决棋子颜色问题  

Solution to Color-changing Problem of Chess Stones by Using Mathematical Experiments

作　　者：麻作军[1] 徐宏武[1] 张骞[1] 

机构地区：[1]陇东学院数学系,甘肃庆阳745000

出　　处：《陇东学院学报》2009年第2期9-12,共4页Journal of Longdong University

基　　金：甘肃省教育厅科研项目(0710-04)

摘　　要：通过对棋子颜色问题建模,定义布尔向量运算系统,分析其性质,改进棋子模型.在此基础上定义了布尔向量的运算周期、扩展周期,解决了初始布尔向量为第一类、第二类不动点的情况.运用数学软件统计了布尔向量的周期,循环节,预测Sn中的布尔向量公倍周期和扩展共倍周期.最后讨论了Sn中1周期点的基本情况.With Color - changing problem of two colors of chess stones modeling, the paper defines operational system of the Boolean vectors, analyses its properties, and improves the chess model. Based on the above analysis, it defines the operational period and the extending period of Boolean vectors, thus it figures out the problem of initial Boolean vectors as the first fixed point and the second fixed point. Then, it works out the Boolean vectors＇ period and its recurring period by applying mathematical software, and it predicts common period doubling and extend common period doubling in Sn . Finally, it discusses the basic situation of 1 - period point in Sn.

关 键 词：棋子问题 布尔向量 不动点 公倍周期 

分 类 号：O141.4[理学—数学]