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

@article{Frabetti2011FiveIO,
  title={Five interpretations of Fa\`a di Bruno's formula},
  author={Alessandra Frabetti and D. Manchon},
  journal={arXiv: Combinatorics},
  year={2011}
}
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. 
11 Citations
Center problem, Abel equation and the Faa di Bruno Hopf algebra for output feedback
  • 7
  • PDF
Noncommutative Bell polynomials, quasideterminants and incidence Hopf algebras
  • 17
  • PDF
Formal Groups, Witt vectors and Free Probability
  • 12
  • PDF
Renormalization: a quasi-shuffle approach
  • 1
  • PDF
Multivariate Bell Polynomials and Derivatives of Composed Functions
  • 1
  • Highly Influenced
  • PDF
SISO Output Affine Feedback Transformation Group and Its Faà di Bruno Hopf Algebra
  • 11
  • PDF
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References

SHOWING 1-10 OF 114 REFERENCES
Faa di Bruno Hopf algebras
  • 15
  • PDF
Incidence Hopf algebras
  • 115
  • Highly Influential
ON BIALGEBRAS AND HOPF ALGEBRAS OF ORIENTED GRAPHS
  • 18
  • PDF
QED Hopf algebras on planar binary trees
  • 66
  • PDF
Encyclopedia of types of algebras 2010
  • 50
  • PDF
Rooted trees and an exponential-like series
  • 35
  • PDF
Prehistory of Faà di Bruno's Formula
  • A. Craik
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 2005
  • 65
Generalized bialgebras and triples of operads
  • 122
  • PDF
...
1
2
3
4
5
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