Geodesic
On log-concavity of a class of generalized Stirling numbers
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are $q$-log-concave or $q$-log-convex under suitable conditions. We further discuss the log-convexity of some linear transformations related to generalized Stirling numbers of the first kind.
DOI : 10.37236/2228
Classification : 05A20, 11B73, 11B83
Mots-clés : Stirling numbers, log-concavity, log-convexity, \(q\)-log-concavity, \(q\)-log-convexity 
@article{10_37236_2228,
     author = {Feng-Zhen Zhao},
     title = {On log-concavity of a class of generalized {Stirling} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {2},
     doi = {10.37236/2228},
     zbl = {1243.05041},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2228/}
}
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Feng-Zhen Zhao. On log-concavity of a class of generalized Stirling numbers. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2228

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