منابع مشابه
Lagrange inversion
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
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1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...
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In [3] we described a technique for solving certain linear operator equations by studying the operator power series de ned by the system. Essential for obtaining explicit solutions is a Lagrange inversion formula for power series with coe¢ cients in an integral domain K. Such a formula can be found in Recursive Matrices and Umbral Calculusby Barnabei, Brini and Nicoletti [1]. J. F. Freemans ...
متن کاملLagrange Inversion: when and how
The aim of the present paper is to show how the Lagrange Inversion Formula (LIF) can be applied in a straight-forward way i) to find the generating function of many combinatorial sequences, ii) to extract the coefficients of a formal power series, iii) to compute combinatorial sums, and iv) to perform the inversion of combinatorial identities. Particular forms of the LIF are studied, in order t...
متن کاملLagrange Inversion and Schur Functions
Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. W...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2016
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.06.018