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.
Constantine and Thomas H
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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.