The behaviour of (n over \(k,\dots ,k,n-ik)c^ i/i!\) is asymptotically normal
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.
scientific article; zbMATH DE number 3873332