(2015) 38:61–73DOI 10.1007/s11139-014-9599-yLog-concavity of the partition functionStephen DeSalvo · Igor PakReceived: 5 November 2013 / Accepted: 21 May 2014 / Published online: 22 August 2014© Springer Science+Business Media New York 2014Abstract We prove that the partition function ...
Pak. Log-concavity of the partition function. The Ramanujan Journal, Volume 38, Issue 1, pp. 61-73, 2015.S.Desalvo and I.Pak, Log-concavity of the partition function, (2013).S.DeSalvo and I.Pak, Log-concavity of the partition function, (2013)....
Log-Concavity of the Partition Function 来自 Springer 喜欢 0 阅读量: 35 作者:S Desalvo,I Pak 摘要: We prove that the partition function \\\(p(n)\\\) is log-concave for all \\\(n>25\\\) . We then extend the results to resolve two related conjectures by Chen and one by Sun. ...
Let $p(n)$ denote the partition function. Desalvo and Pak proved the log-concavity of $p(n)$ for $n>25$ and the inequality $\frac{p(n-1)}{p(n)}\left(1+\frac{1}{n}\right)>\frac{p(n)}{p(n+1)}$ for $n>1$. Let $r(n)=\sqrt[n]{p(n)/n}$ and $\Delta$ be ...
The main results from this connection are: dominance of allocations, optimal partition, upper and lower bounds on throughput, consistency of the IPA ... SR Tayur - 《Queueing Systems》 被引量: 49发表: 1992年 Approximately Sampling Elements with Fixed Rank in Graded Posets log-concavity, which...
of log-concave sequence are derived by the connection. Therefore, the open problem proposed by Schmidt and Simion is partially solved. In combinatorics, the combinatorial polynomials and log-concavity for some combinatorial sequences are investigated by spline theory. With the well developed spline ...
comesfromthefactthatitrepresents(uptoanadditiveconstantinvolvingthelogarithmofthepartitionfunction)theHamiltonianorenergyofaphysicalsystemunderaGibbsmeasure;anditsimportanceinstatisticscomesfromthefactthatitrepresentsthelog-likelihoodfunctioninthenonparametricinferenceproblemofdensityestimation.Theaveragevalueoftheinformation...
Pak, Log-concavity of the partition function. Ramanujan J. 38 (2015), 61-73.S. DeSalvo and I. Pak, Log-concavity of the partition function, Ra- manujan J. 38 (1) (2015) 61-73.S. DeSalvo and I. Pak, Log-concavity of the partition function, Ramanujan. J 38 (2015), no. 1,...
r-log-concavityPartition functionHardy-Ramanujan-Rademacher formulaLet be the operator given by . A sequence is called asymptotically r-log-concave if are non-negative sequences for and some integer N. Let p(n) be the number of integer partitions of n. We prove that the sequence is ...
Log-concavity of the overpartition functiondoi:10.1007/S11139-015-9762-0Benjamin EngelSpringer USB. Engel, Log-concavity of the overpartition function, Ramanujan J. 43 (2) (2017) 229-241.