【作者】 蒋茂勇；

【导师】 马欣荣；

【作者基本信息】 苏州大学 ， 应用数学， 2001， 硕士

【摘要】 本文共分五章，主题是研究拉格郎日反演公式所包含的一个拟卷积公式和它的指数结构以及组合证明。 第一章对拉格朗日反演在Riordan群理论中的应用进行了介绍，证明了一个组合等式： 第二章通过对拉格朗日反演定理本身的分析，得到一个对任意的形式幂级数都适用的三个拟卷积公式，这些公式体现了任意能在零点解析的函数的内在性质。文章给出这些拟卷积公式的一些应用。 第三章讨论指数公式的组合意义，得到了一个新的结果（定理3.2.1），并讨论它们的应用。 第四章给出拟卷积公式C_t^n-1Φⁿ（t）=sum from k=1 to n(（1/k）C_t^k-1Φ^k（t）C_t^n-kΦ^n-k（t）)的组合证明，建立了一种新的数学模型——克隆羊模型。克隆羊模型给公式2.1.3中的C_t^n-1Φⁿ（t），C_tⁿΦⁿ（t）以直观的组合描述。文章进一步证明了克隆学模型的基本性质，借助于移位变换，完成对公式的全部证明。 第五章为结论。更多还原

【Abstract】 This thesis is composed of four sections, and its theme is concerned with Lagrange inversion formula In section one, some applications of Lagrange inversion related to Roridan group is sketched. A combinatorial identity is obtained: (~z:)=:~z 2r扟32(n-r)-rn-iJ As main result of this paper, in section two, the convolution梩ype identities emerge from our discussion about Lagrange formula whom in author 憇 view can be taken as the inherent characteristic of Lagrange formula but have been ignored fOi so long time. Some old and new applications of those formula are also investigated in great details. The section three discusses further the convolution梩ype identities obtained in section two and finally sets up one corresponding exponential formula, displayed in Theorem 3.2.1. It抯 new applications to combinatorics are presented. Finally, a combinatorial proof of the formula is provided in section four after a new mathematical model-sheep-clones model having been defined and discussed. In section five we restate the results that we have obtained. Maoyong Jiang Directed by associate professor Ma Xinrong更多还原