A COMBINATORIAL THEORY OF FORMAL SERIES
A COMBINATORIAL THEORY OF FORMAL SERIES
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DOI：
10.1016/0001-8708(81)90052-9
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发表时间：
1981-01-01
影响因子：
1.7
通讯作者：
JOYAL, A
中科院分区：
文献类型：
--
作者：
JOYAL, A
本文提出了形式幂级数的一种组合理论。形式幂级数的组合解释是基于结构种类的概念。给出了Cayley标号树个数公式的一个新的证明，以及一个新的组合证明（由于G。Labelle）的拉格朗日反演公式。波利亚的同构类结构的计数理论是完全更新。描述了计算循环指数多项式的递归方法。隐函数定理的一个组合版本的陈述和证明。最后，本文对余代数在组合学中的应用进行了一般性的考虑。
This paper presents a combinatorial theory of formal power series. The combinatorial interpretation of formal power series is based on the concept of species of structures. A categorical approach is used to formulate it. A new proof of Cayley's formula for the number of labelled trees is given as well as a new combinatorial proof (due to G. Labelle) of Lagrange's inversion formula. Polya's enumeration theory of isomorphism classes of structures is entirely renewed. Recursive methods for computing cycle index polynomials are described. A combinatorial version of the implicit function theorem is stated and proved. The paper ends with general considerations on the use of coalgebras in combinatorics.