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ON MULTIPLE AND INFINITE LOGCONCAVITY
"... Abstract. Following Boros–Moll, a sequence (an) is mlogconcave if Lj(an)> 0 for all j = 0, 1,...,m. Here, L is the operator defined by L(an) = a2n − an−1an+1. By a criterion of Craven–Csordas and McNamara–Sagan it is known that a sequence is ∞logconcave if it satisfies the stronger inequali ..."
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Abstract. Following Boros–Moll, a sequence (an) is mlogconcave if Lj(an)> 0 for all j = 0, 1,...,m. Here, L is the operator defined by L(an) = a2n − an−1an+1. By a criterion of Craven–Csordas and McNamara–Sagan it is known that a sequence is ∞logconcave if it satisfies the stronger inequal
Logconcavity and LCpositivity
, 2006
"... A triangle {a(n,k)}0≤k≤n of nonnegative numbers is LCpositive if for each r, the sequence of polynomials ∑ n k=r a(n,k)qk is qlogconcave. It is double LCpositive if both triangles {a(n,k)} and {a(n,n − k)} are LCpositive. We show that if {a(n,k)} is LCpositive then the logconcavity of the seq ..."
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A triangle {a(n,k)}0≤k≤n of nonnegative numbers is LCpositive if for each r, the sequence of polynomials ∑ n k=r a(n,k)qk is qlogconcave. It is double LCpositive if both triangles {a(n,k)} and {a(n,n − k)} are LCpositive. We show that if {a(n,k)} is LCpositive then the logconcavity
LOGCONCAVITY OF THE PARTITION FUNCTION
"... Abstract. We prove that the partition function p(n) is logconcave for all n> 25. We then extend the results to resolve two related conjectures by Chen and one by Sun. The proofs are based on Lehmer’s estimates on the remainders of the Hardy–Ramanujan and the Rademacher series for p(n). ..."
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Cited by 2 (0 self)
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Abstract. We prove that the partition function p(n) is logconcave for all n> 25. We then extend the results to resolve two related conjectures by Chen and one by Sun. The proofs are based on Lehmer’s estimates on the remainders of the Hardy–Ramanujan and the Rademacher series for p(n).
LogConcavity: a review
"... Abstract: We review and formulate results concerning logconcavity and stronglogconcavity in both discrete and continuous settings. We show how preservation of logconcavity and strongly logconcavity on R under convolution follows from a fundamental monotonicity result of Efron (1969). We provid ..."
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Abstract: We review and formulate results concerning logconcavity and stronglogconcavity in both discrete and continuous settings. We show how preservation of logconcavity and strongly logconcavity on R under convolution follows from a fundamental monotonicity result of Efron (1969). We
LogConcavity Properties of Minkowski Valuations
"... Abstract. New Orlicz Brunn–Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical logconcavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine prev ..."
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Abstract. New Orlicz Brunn–Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical logconcavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine
A computer proof of Moll’s logconcavity conjecture
 PROCEEDINGS OF THE AMS
, 2007
"... In a study on quartic integrals, Moll met a specialized family of Jacobi polynomials. He conjectured that the corresponding coefficient sequences are logconcave. In this paper we settle Moll’s conjecture by a nontrivial usage of computer algebra. ..."
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Cited by 33 (5 self)
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In a study on quartic integrals, Moll met a specialized family of Jacobi polynomials. He conjectured that the corresponding coefficient sequences are logconcave. In this paper we settle Moll’s conjecture by a nontrivial usage of computer algebra.
Insertion sequences
 Microbiol Mol. Biol. Rev
, 1998
"... These include: Receive: RSS Feeds, eTOCs, free email alerts (when new articles cite this article), more» Downloaded from ..."
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Cited by 426 (3 self)
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These include: Receive: RSS Feeds, eTOCs, free email alerts (when new articles cite this article), more» Downloaded from
Roles of LogConcavity, . . .
, 2001
"... In this paper we will develop a systematic method to answer the questions (Q1)(Q2)(Q3)(Q4) (stated in Section 1) with complete generality. As a result, we can solve the difficulties (D1)(D2) (discussed in Section 1) without uncertainty. For these purposes we will introduce certain classes of growth ..."
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of growth functions u and apply the Legendre transform to obtain a sequence which leads to the weight sequence {α(n)} first studied by Cochran et al. [6]. The notion of (nearly) equivalent functions, (nearly) equivalent sequences and dual Legendre functions will be defined in a very natural way
Results 1  10
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1,039,700