| 关于含r对k间隔的组合数 |
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| 引用本文： | 刘玉记. 关于含r对k间隔的组合数[J]. 佛山科学技术学院学报(自然科学版), 1995, 0(4) |
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| 作者姓名： | 刘玉记 |
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| 作者单位： | 岳阳师专数学系 岳阳 |
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| 摘 要： | 记 f(n,m)为从排列在一直线上的 n 个元素中选取 m 个元素且恰含 r 对 k 间隔元素的选取方式数.g_k~r(n,m)为从排列在圆周上的 n 个元素中选取 m 个元素且恰含 r 对 k 间隔元素的选取方式数,给出了 f_k~r(n,m)及 g_k~r(n,m)的递归关系式和卷积形式表达式,在 k=0时得到 f_0~r(n,m)与 g_0~r(n,m)的显式.
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| 关 键 词： | 组合数 k 间隔 环上 k 间隔 显式 |
On the Number of Combinations with r Pair k-Separations |
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| Liu Yuji. On the Number of Combinations with r Pair k-Separations[J]. Journal of Foshan University(Natural Science Edition), 1995, 0(4) |
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| Authors: | Liu Yuji |
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| Affiliation: | Liu Yuji Department of Mathematics,Yueyang Teachers College,Yueyang 414000 |
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| Abstract: | Let f_k~r(n,m)denote the number of ways of selecting rn objects from n objects arranged in a line with r pair k-separations and g_k~r (n,m) denote the number of ways of selecting m objects from n ob- jects arranged in a circle.If k=0,the formulas of f_o~r (n,m) and g_o~r(n,m) were given.In addition,the counting formulas of f_k~r(n,m) and g_k~r(n,m) in the form of multifold convolutions by means of the inductive deduction were presented. |
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| Keywords: | number of combinations k-separation k-separations in a circle inductive formula |
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