Name
Abstract | ||
|---|---|---|
We study linear recurrences of Eulerian type of the formPn(v)=(α(v)n+γ(v))Pn−1(v)+β(v)(1−v)Pn−1′(v)(n⩾1), with P0(v) given, where α(v),β(v) and γ(v) are in most cases polynomials of low degrees. We characterize the various limit laws of the coefficients of Pn(v) for large n using the method of moments and analytic combinatorial tools under varying α(v),β(v) and γ(v), and apply our results to more than two hundred of concrete examples when β(v)≠0 and more than three hundred when β(v)=0 that we gathered from the literature and from Sloane's OEIS database. The limit laws and the convergence rates we worked out are almost all new and include normal, half-normal, Rayleigh, beta, Poisson, negative binomial, Mittag-Leffler, Bernoulli, etc., showing the surprising richness and diversity of such a simple framework, as well as the power of the approaches used. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.aam.2019.101960 | Advances in Applied Mathematics |
Keywords | Field | DocType |
05A05,05A10,05A15,05A16,05E15,11B83,30E15,35F05,39A10,41A60,60C05,60F05,60F15 | Discrete mathematics,Limit of a function,Combinatorics,Polynomial,Eulerian path,Negative binomial distribution,Poisson distribution,Mathematics,Asymptotic distribution,Bernoulli's principle | Journal |
Volume | ISSN | Citations |
112 | 0196-8858 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hsien-Kuei Hwang | 1 | 365 | 38.02 |
| Hua-Huai Chern | 2 | 78 | 7.25 |
| Guan-Huei Duh | 3 | 0 | 0.68 |