TY - JOUR
T1 - Concavity properties and a generating function for stirling numbers
AU - Lieb, Elliott H.
PY - 1968/9
Y1 - 1968/9
N2 - The Stirling numbers of the first kind, SNk, and of the second kind, δNk, are shown to be strongly logarithmically concave as functions of k for fixed N. This result is stronger than the unimodality conjecture which was heretofore proved only for δNk (Harper). We also introduce a generating function for the δNk which is different from the conventional one but which has a relatively simple closed form expression.
AB - The Stirling numbers of the first kind, SNk, and of the second kind, δNk, are shown to be strongly logarithmically concave as functions of k for fixed N. This result is stronger than the unimodality conjecture which was heretofore proved only for δNk (Harper). We also introduce a generating function for the δNk which is different from the conventional one but which has a relatively simple closed form expression.
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U2 - 10.1016/S0021-9800(68)80057-2
DO - 10.1016/S0021-9800(68)80057-2
M3 - Article
AN - SCOPUS:0000746209
VL - 5
SP - 203
EP - 206
JO - Journal of Combinatorial Theory
JF - Journal of Combinatorial Theory
SN - 0021-9800
IS - 2
ER -