On the number of words with restrictions on the number of symbols

被引：0
|
作者：
Becher, Veronica [1 ,2 ,3 ]
Cesaratto, Eda [3 ,4 ]
机构：
[1] Fac Ciencias Exactas & Nat Buenos Aires, Dept Comp, Buenos Aires, DF, Argentina
[2] ICC Univ Buenos Aires, Buenos Aires, DF, Argentina
[3] Consejo Nacl Invest Cient & Tecn, Buenos Aires, DF, Argentina
[4] Univ Nac Gral Sarmiento, Los Polvorines, Buenos Aires, Argentina
来源：
ADVANCES IN APPLIED MATHEMATICS | 2022年 / 136卷
关键词：
Poisson distribution; Laplace method for sums; Stirling numbers of the second kind; Combinatorics on; STIRLING NUMBERS;
D O I：
10.1016/j.aam.2022.102321
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that, in an alphabet of n symbols, the number of words of length n whose number of different symbols is away from (1 - 1/e)n, which is the value expected by the Poisson distribution, has exponential decay in n. We use Laplace's method for sums and known bounds of Stirling numbers of the second kind. We express our result in terms of inequalities.(c) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页数：20
相关论文
共 50 条
12345