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.
Five interpretations of Fa\`a di Bruno's formula
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abstract
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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2026 1verdicts
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Discrete Fa\`a di Bruno via M\"obius Inversion
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.