Name
Abstract | ||
|---|---|---|
A "hybrid method", dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions-this, even in the case when the unit circle is a natural boundary. A prime application is to coefficients of several types of infinite product generating functions, for which full asymptotic expansions (involving periodic fluctuations at higher orders) can be derived. Examples relative to permutations, trees, and polynomials over finite fields are treated in this way. |
Year | Venue | Keywords |
|---|---|---|
2006 | ELECTRONIC JOURNAL OF COMBINATORICS | higher order,asymptotic expansion,satisfiability,generating function |
Field | DocType | Volume |
Discrete mathematics,Generating function,Combinatorics,Finite field,Infinite product,Polynomial,Singularity function,Asymptotic analysis,Unit circle,Asymptotic analysis,Mathematics | Journal | 13.0 |
Issue | ISSN | Citations |
1.0 | 1077-8926 | 5 |
PageRank | References | Authors |
0.93 | 12 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Philippe Flajolet | 1 | 3466 | 523.08 |
| Éric Fusy | 2 | 198 | 21.95 |
| Xavier Gourdon | 3 | 229 | 22.85 |
| Daniel Panario | 4 | 438 | 63.88 |
| Nicolas Pouyanne | 5 | 14 | 2.73 |