Concavity properties and a generating function for stirling numbers

Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)203-206
Number of pages4
JournalJournal of Combinatorial Theory
Issue number2
StatePublished - Sep 1968


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