不相邻组合计数问题之新解法探讨

New Multiple Solutions to Enumerative Problem on Non-adjacent Combination

不相邻组合计数问题是组合数学中的一个典型问题.关于该问题,现有教材普遍提供的是一种学生不易理解的采用拉伸技巧的解法.利用常见的放球模型和实际生活中的占位模型,巧妙构造该问题的四种别具特色的新解法,有助于学生理解不相邻组合计数问题以及相关的组合计数技巧.

Enumerative problem on non-adjacent combination is a typical problem in combinatorics.However,an unique solution by using stretching skills is given in the present course books,which is difficult for students to understand.In this paper,we give four distinctive new solutions based on common combinatorial models.