Geodesic
Coefficients of functional compositions often grow smoothly
The electronic journal of combinatorics, Tome 15 (2008)
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The coefficients of a power series $A(x)$ are smooth if $a_{n-1}/a_n$ approaches a limit. If $A(x)=F(G(x))$ and $f_n^{1/n}$ approaches a limit, then the coefficients of $A(x)$ are often smooth. We use this to show that the coefficients of the exponential generating function for graphs embeddable on a given surface are smooth, settling a problem of McDiarmid.
DOI : 10.37236/745
Classification : 05A16, 05A15, 05C30
Mots-clés : coefficients of power series, exponential generating function, graphs embeddable on a surface 
@article{10_37236_745,
     author = {Edward A. Bender and E. Rodney Canfield and L. Bruce Richmond},
     title = {Coefficients of functional compositions often grow smoothly},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/745},
     zbl = {1158.05303},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/745/}
}
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Edward A. Bender; E. Rodney Canfield; L. Bruce Richmond. Coefficients of functional compositions often grow smoothly. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/745

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