Concavity properties and a generating function for stirling numbers

Elliott H. Lieb

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

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
Volume5
Issue number2
DOIs
StatePublished - Sep 1968

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