Concavity properties and a generating function for stirling numbers

Elliott H. Lieb

doi:10.1016/S0021-9800(68)80057-2

Concavity properties and a generating function for stirling numbers

Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

The Stirling numbers of the first kind, S_N^k, and of the second kind, δ_N^k, 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 δ_N^k (Harper). We also introduce a generating function for the δ_N^k which is different from the conventional one but which has a relatively simple closed form expression.

Original language	English (US)
Pages (from-to)	203-206
Number of pages	4
Journal	Journal of Combinatorial Theory
Volume	5
Issue number	2
DOIs	https://doi.org/10.1016/S0021-9800(68)80057-2
State	Published - Sep 1968

Access to Document

10.1016/S0021-9800(68)80057-2

Fingerprint Dive into the research topics of 'Concavity properties and a generating function for stirling numbers'. Together they form a unique fingerprint.

Cite this

@article{e3932c2515574c4f89cc03f43b1bc697,

title = "Concavity properties and a generating function for stirling numbers",

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.",

author = "Lieb, {Elliott H.}",

year = "1968",

month = sep,

doi = "10.1016/S0021-9800(68)80057-2",

language = "English (US)",

volume = "5",

pages = "203--206",

journal = "Journal of Combinatorial Theory",

issn = "0021-9800",

publisher = "Academic Press Inc.",

number = "2",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0000746209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000746209&partnerID=8YFLogxK

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 -