Concavity properties for certain linear combinations of Stirling numbers
نویسندگان
چکیده
منابع مشابه
Log-concavity of Stirling Numbers and Unimodality of Stirling Distributions
A series of inequalities involving Stirling numbers of the first and second kinds with adjacent indices are obtained. Some of them show log-concavity of Stirling numbers in three different directions. The inequalities are used to prove unimodality or strong unimodality of all the subfamilies of Stirling probability functions. Some additional applications are also presented.
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The numbers ẽp(k, n) defined as min(νp(S(k, j)j!) : j ≥ n) appear frequently in algebraic topology. Here S(k, j) is the Stirling number of the second kind, and νp(−) the exponent of p. Let sp(n) = n− 1 + νp([n/p]!). The author and Sun proved that if L is sufficiently large, then ẽp((p− 1)p + n− 1, n) ≥ sp(n). In this paper, we determine the set of integers n for which ẽp((p− 1)p + n − 1, n) = s...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1973
ISSN: 0004-9735
DOI: 10.1017/s1446788700012891