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

2010/09/28 by Matthias Aschenbrenner, Aschenbrenner, Matthias
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Topics in Algebra #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.CO #math.CV

paper · pdf · doi:10.48550/arxiv.1009.5518

29 pp

openalex publication_date 2010/09/28 · arxiv created 2011/11/09 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A proof for 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.

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