Asymptotics of the modes of the ordered Stirling numbers
Istv\'an Mez\H{o}
TL;DR
This paper investigates the asymptotic behavior of the modes of ordered Stirling numbers, providing new insights into their distribution which were previously unknown, especially compared to the well-studied Stirling numbers.
Contribution
It offers the first estimations of the modes of ordered Stirling numbers, extending understanding beyond the classical Stirling numbers.
Findings
Derived asymptotic estimates for the modes of ordered Stirling numbers
Extended analysis to generalizations of these numbers
Provided new bounds and approximations for the modes
Abstract
It is known that the Stirling numbers as well as the ordered Stirling numbers form log-concave sequences. Although in the first case there are many estimations about the mode, for the ordered Stirling numbers such estimations are not known. In this short note we study this problem and some of its generalizations.
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Taxonomy
TopicsOrbital Angular Momentum in Optics · Mechanical and Optical Resonators · Advanced Fiber Optic Sensors