The behaviour of (n over \(k,\dots ,k,n-ik)c^ i/i!\) is asymptotically normal
type: Item
instance of: scholarly article
title: The behaviour of (n over \(k,\dots ,k,n-ik)c^ i/i!\) is asymptotically normal
zbMATH Open document ID: 0548.05003
DOI: 10.1016/0012-365X(84)90165-1
author: Andrzej Ruciński
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let N(n,i) denote the weighted multinomial coefficient \(\left( \begin{matrix} n\\ k,...,k,n-ik\end{matrix} \right)c^ i/i! i=0,...,\lfloor n/k\rfloor.\) The author rederives T. Zaslavsky's observation that the generating function \(N(x)=\sum N(n,i)x^ i\) has all zeros real and negative and then, using a method developed by \textit{L. H. Harper} [Ann. Math. Stat. 38, 410-414 (1967; Zbl 0154.437)], deduces that the ''probabilities'' \(N(n,i)/\sum N(n,i) (i=0,...,\lfloor n/k\rfloor)\) are asymptotically normally distributed. The author also strengthens a lower bound, due to the reviewer, on the variance of the number of edges in a matching chosen at random from a graph.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 60C05
zbMATH DE Number: 3873332
zbMATH Keywords: asymptotic normality
zbMATH Keywords: multinomial coefficients
zbMATH Keywords: matchings
zbMATH Keywords: generating function
MaRDI profile type: Publication
cites work: Q3852212
cites work: On a general class of graph polynomials
cites work: Matching behaviour is asymptotically normal
cites work: Stirling Behavior is Asymptotically Normal
cites work: Theory of monomer-dimer systems
cites work: Q3752420
description: scientific article; zbMATH DE number 3873332