Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Logconcavity, twice-logconcavity and Turán-type inequalities

Logconcavity, twice-logconcavity and Turán-type inequalities Ann Oper Res https://doi.org/10.1007/s10479-018-2923-y S.I.: STOCHASTIC MODELING AND OPTIMIZATION, IN MEMORY OF ANDRÁS PRÉKOPA Logconcavity, twice-logconcavity and Turán-type inequalities 1 2 Anh Ninh · Minh Pham © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper presents a brief review of the logconcavity of some compound distri- butions and its relationship to Turán-type inequalities. Further, we introduce a new concept of twice-logconcavity (twice-logconvexity) and show that many discrete probability distri- butions and combinatorial sequences are twice-logconcave. These results are closely related to other areas of mathematics such as combinatorics and analysis. Keywords Compound Poisson · Logconcavity · Turán inequalities · Divided differences 1 Introduction In 1912, Fekete introduced the notion of an r-times positive sequence, which is known as twice-positive sequence, or, log-concave sequence for r = 2. A sequence of nonnegative elements... a , a , a ,... is said to be r-times positive if the matrix −2 −1 0 ⎛ ⎞ . . . . . . . . . ⎜ ⎟ ⎜ ⎟ ⎜ . ⎟ a a a ⎜ 0 1 2 ⎟ ⎜ ⎟ . . ⎜ ⎟ A = . . , . . ⎜ a a a ⎟ −1 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

Logconcavity, twice-logconcavity and Turán-type inequalities

Annals of Operations Research , Volume OnlineFirst – Jun 6, 2018

Loading next page...
 
/lp/springer_journal/logconcavity-twice-logconcavity-and-tur-n-type-inequalities-rL0E7Iycu9
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
DOI
10.1007/s10479-018-2923-y
Publisher site
See Article on Publisher Site

Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2923-y S.I.: STOCHASTIC MODELING AND OPTIMIZATION, IN MEMORY OF ANDRÁS PRÉKOPA Logconcavity, twice-logconcavity and Turán-type inequalities 1 2 Anh Ninh · Minh Pham © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract This paper presents a brief review of the logconcavity of some compound distri- butions and its relationship to Turán-type inequalities. Further, we introduce a new concept of twice-logconcavity (twice-logconvexity) and show that many discrete probability distri- butions and combinatorial sequences are twice-logconcave. These results are closely related to other areas of mathematics such as combinatorics and analysis. Keywords Compound Poisson · Logconcavity · Turán inequalities · Divided differences 1 Introduction In 1912, Fekete introduced the notion of an r-times positive sequence, which is known as twice-positive sequence, or, log-concave sequence for r = 2. A sequence of nonnegative elements... a , a , a ,... is said to be r-times positive if the matrix −2 −1 0 ⎛ ⎞ . . . . . . . . . ⎜ ⎟ ⎜ ⎟ ⎜ . ⎟ a a a ⎜ 0 1 2 ⎟ ⎜ ⎟ . . ⎜ ⎟ A = . . , . . ⎜ a a a ⎟ −1

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 6, 2018

References