Combinatorics of partial derivatives

Electronic Journal of Combinatorics

Volumn 13, Issue 1 R, 2006, Pages 1-13

  Hardy, Michael ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30344479471     PISSN: 10778926     EISSN: 10778926     Source Type: Journal    
DOI: 10.37236/1027     Document Type: Article

References (20)

1. L.F.A. Arbogast, Du Calcul des Dérivations, Levrault, Strasbourg, 1800.
2. F. Faà di Bruno, Sullo Sviluppo delle Funzioni, Annali di Scienze Matematiche e Fisiche 6, 1855 pp. 479-480.
3. F. Faà di Bruno, Note sur un nouvelle formule de calcul différentiel, Quarterly Journal of Pure and Applied Mathematics, 1, 1857, pp. 359-360.
4. L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Reidel, Dordrecht-Holland/Boston, 1974.
5. G.M. Constantine and T.H. Savits, A Multivariate Faà di Bruno Formula with Applications, Transactions of the American Mathematical Society, 348, 1996 pp. 503-520.
6. A. Craik, Prehistory of Faa di Bruno's Formula, American Mathematical Monthly, 112 (2), February 2005, pp. 119-130.
7. R.A. Fisher and J. Wishart, The derivation of the pattern formulae of two-way partitions from those of simpler patterns, Proceedings of the London Mathematical Society, Series 2, 33, 1931, pp. 195-208.
8. W.P. Johnson, The Curious History of Faà di Bruno's Formula, Am. Math. Monthly 109, 2002, pp. 217-227.
9. R. Leipnik and T. Reid, Multivariable Faa di Bruno Formulas, Electronic Proceedings of the Ninth Annual International Conference on Technology in Collegiate Mathematics, http://archives.math.utk.edu/ICTCM/EP-9.html#C23.
10. R. Mishkov, Generalization of the Formula of Faa di Bruno for a Composite Function with a Vector Argument, International Journal of Mathematical Sciences, 24, 2000, pp. 481-491.
11. S. Noschese and P.E. Ricci, Differentiation of Multivariable Composite Functions and Bell Polynomials, Journal of Computational Analysis and Applications, 5, 2003, pp. 333-340.
12. G-C. Rota, The Number of Partitions of a Set, Am. Math. Monthly 71, 1964, pp. 498-504.
13. C-C. Rota, Geometric Probability, Mathematical Intelligencer, 20 (4), 1998, pp. 11-16.
14. T.P. Speed, Cumulants and Partition Lattices, Australian Journal of Statistics, 25 (2), 1983, pp. 378-388.
15. R.P. Stanley, Enumerative Combinatorics, Volume 2, Cambridge University Press, Cambridge, 1999.
16. T.N. Thiele, Forlæsinger over Almindelig Iagttagelselære, Reitzel, Copenhagen, 1889.
17. T.N. Thiele, Theory of Observations, Layton, London, 1903.
18. Reprinted in Annals of Mathematical Statistics, 2, 1931, pp. 165-308.
19. W.C. Yang, Derivatives are Essentially Integer Partitions, Discrete Mathematics, 222, 2000, pp. 235-245.
20. D. Zeilberger, "Toward a Combinatorial Proof of the Jacobian Conjecture", in Lecture Notes in Mathematics v. 1234, Combinatoire Énumérative, Springer-Verlag, Berlin, 1986.