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A Determinant Identity Implying the Lagrange–Good Inversion Formula

Part of: Basic linear algebra Combinatorics

Published online by Cambridge University Press:  13 June 2016

Jianfeng Huang  and
Xinrong Ma
Jianfeng Huang
Affiliation:
Department of Mathematics, Soochow University, SuZhou 215006, People's Republic of China (xrma@suda.edu.cn)
Xinrong Ma
Affiliation:
Department of Mathematics, Soochow University, SuZhou 215006, People's Republic of China (xrma@suda.edu.cn)
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Abstract

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In this paper a determinant identity is established, from which a simple proof of the multivariate Lagrange–Good inversion formula follows directly. Further discussion on a discrete analogue of the Lagrange–Good inversion formula is also presented.

Keywords

Lagrange–BürmannLagrange–Goodinversion formulamatrix inversionformal derivativeformal power series

MSC classification

Secondary: 05A15: Exact enumeration problems, generating functions 15A23: Factorization of matrices
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 165 - 176
Copyright
Copyright © Edinburgh Mathematical Society 2016