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Journal article
A Class of Polynomial Recurrences Resulting in (n/log n, n/log2n) – Asymptotic Normality
La Matematica, v 3, pp 1069-1084
15 Jul 2024
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Abstract
We consider sequences of polynomials that satisfy differential–difference recurrences. Polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. We identify a class of polynomial recurrences that lead to a normal law with the expected value and the variance proportional to
and
, respectively. Examples include Stirling numbers of the second kind and other polynomials concerning set partitions as well as polynomials related to Whitney numbers of Dowling lattices.
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Details
- Title
- A Class of Polynomial Recurrences Resulting in (n/log n, n/log2n) – Asymptotic Normality
- Creators
- Pawel Hitczenko (Corresponding Author) - Drexel University, Mathematics
- Publication Details
- La Matematica, v 3, pp 1069-1084
- Publisher
- Springer Nature
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Scopus ID
- 2-s2.0-85198509034
- Other Identifier
- 991021893411704721