The Convolution-type Identity Of Lagrange Inversion Formula And It's Combiatorial Proof

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...