论文标题
离散数学
Discrete Mathematics
论文作者
论文摘要
本工作的目的是在基本\ textit {枚举代数组合}上提供30美元的入门课程的简短和柔和的教学笔记。我们完全采用\ textit {rota way}。主题被组织成一个合适的序列，使我们能够通过基本过程从前面的序列得出任何结果。 \ textit {组合系数}的定义仅通过其\ textit {combinatorial含义}。公式/结果的推导技术建立在构造和两个一般和基本原理/方法的基础上： - \ textit {bad element}方法（\ textit {递归}公式）。正如读者应识别的那样，不良元素方法可能被视为\ textit {条件概率}想法的组合伴侣。 - \ textIt {夸大}原理（对于\ textit {close form}公式）。 因此，\ textIt {无计算}在\ textIt {praces}中需要：\ textit {计算公式是组合构造的副产品}。我们试图提供一个独立的演讲：唯一的先决条件是标准的高中数学。我们将自己限制在\ textit {combinatorial视图}：我们邀请读者绘制（明显的）\ textit {概率解释}。
The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of \textit{combinatorial coefficients} are just by their \textit{combinatorial meaning}. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods: - The \textit{bad element} method (for \textit{recursive} formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of \textit{conditional probability}. - The \textit{overcounting} principle (for \textit{close form} formulae). Therefore, \textit{no computation} is required in \textit{proofs}: \textit{computation formulae are byproducts of combinatorial constructions}. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the \textit{combinatorial point of view}: we invite the reader to draw the (obvious) \textit{probabilistic interpretations}.
