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math.CO2022
Variations of Central Limit Theorems and Stirling numbers of the First Kind
Bernhard Heim, Markus Neuhauser
We construct a new parametrization of double sequences between and $A_{n,k}(1)= \frac{1}{n!}\stirl{n}{k}$, where $\stirl{n}{k}…
math.CO2022
Turán Inequalities for Infinite Product Generating Functions
Bernhard Heim, Markus Neuhauser
In the s, Nicolas proved that the partition function is log-concave for . In \cite{HNT21}, a precise conjecture on the log-concavity for the plane partition f…
math.CO2022
Log-Concavity of Infinite Product Generating Functions
Bernhard Heim, Markus Neuhauser
In the s Nicolas proved that the coefficients defined by the generating function \begin{equation*} \sum_{n=0}^{\infty} p_d(n) \, q^n = \prod_{n=1}^{\infty} \left( 1-…