Multivariate asymptotic analysis of set partitions: Focus on blocks of fixed size

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Guy Louchard¹ 

[1] Université Libre de Bruxelles, Département d’Informatique

关键词: Set partitions;    Bell numbers;    Asymptotics;    Saddle point method;    Multiseries expansions;    Analytic combinatorics;   

DOI  :  10.13069/jacodesmath.37019

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Using the Saddle point method and multiseries expansions, we obtain from the exponential formulaand Cauchy’s integral formula, asymptotic results for the number T(n, m, k) of partitions of n labeledobjects with m blocks of fixed size k. We analyze the central and non-central region. In the regionm = n/k − nα, 1 > α > 1/2, we analyze the dependence of T(n, m, k) on α. This paper fits withinthe framework of Analytic Combinatorics.

【 授权许可】

CC BY