Asymptotic enumeration by Khintchine-Meinardus method: Necessary and sufficient conditions for sub exponential growth
Combinatorics
2017-06-28 v2
Abstract
In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary and suffcient condition for normal local limit theorem for aforementioned structures. The latter result allows to encompass in our study structures with weights having gaps in their supports.
Keywords
Cite
@article{arxiv.1606.08016,
title = {Asymptotic enumeration by Khintchine-Meinardus method: Necessary and sufficient conditions for sub exponential growth},
author = {Boris Granovsky},
journal= {arXiv preprint arXiv:1606.08016},
year = {2017}
}
Comments
30 pages. This is a revised version that incorporates changes implied by remarks of a referee