Logarithms of iteration matrices, and proof of a conjecture by Shadrin and Zvonkine

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Abstract

A proof of a conjecture by Shadrin and Zvonkine, relating the entries of a matrix arising in the study of Hurwitz numbers to a certain sequence of rational numbers, is given. The main tools used are iteration matrices of formal power series and their (matrix) logarithms.

Keywords

Iteration matrices
Matrix logarithm
Iterative logarithm
Hurwitz numbers

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Partially supported by a grant from the National Science Foundation.