What Is Enumerative Combinatorics
What Is Enumerative Combinatorics
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DOI：
10.1007/978-1-4615-9763-6_1
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发表时间：
1986-07
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影响因子：
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通讯作者：
Richard P. Stanley
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文献类型：
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作者：
Richard P. Stanley
计数组合学的基本问题是计算有限集合中元素的个数。通常给定无限类有限集合Si，其中在某个索引集合I上变化（例如非负整数），并且我们希望“同时”计算每个Si的元素数量$>（i）。哲学上的困难就出现了。“数”Si元素的个数是什么意思？这个问题没有明确的答案。只有通过经验，人们才能发展出一个概念，即计数函数的“确定”是什么意思。
The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite setsSiwhereiranges over some index setI(such as the nonnegative integers ℕ), and we wish to count the number ƒ(i) of elements of eachSi“simultaneously.” Immediate philosophical difficulties arise. What does it mean to “count” the number of elements ofSi? There is no definitive answer to this question. Only through experience does one develop an idea of what is meant by a “determination” of a counting function ƒ(i).