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Five interpretations of Fa\`a di Bruno's formula

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arxiv 1402.5551 v1 pith:VXRMYHFD submitted 2014-02-22 math.CO math-phmath.GRmath.MPmath.QA

Alessandra Frabetti (ICJ) , Dominique Manchon This is my paper · ORCID
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keywords algebrasbrunofiveformulainterpretationscombinatoricscompositioncomputes
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In these lectures we present five interpretations of the Fa' di Bruno formula which computes the n-th derivative of the composition of two functions of one variable: in terms of groups, Lie algebras and Hopf algebras, in combinatorics and within operads.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Discrete Fa\`a di Bruno via M\"obius Inversion

    math.CO 2026-07 accept novelty 7.0 of 10

    Composing discrete Taylor expansions and applying Möbius inversion yields a covering-indexed Faà di Bruno formula that deforms flatly into the classical partition form for Fréchet derivatives.

  2. Corecursive Coding of High Computational Derivatives and Power Series

    cs.PL 2025-01 conditional novelty 4.0 of 10

    A Haskell tutorial for deriving infinite derivative chains and power series through lazy corecursion, including composition, reversion, and a Stirling-series example.

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