Log-concavity of the partition function. The Ramanujan Journal (10 2013). 4, 5S.DeSalvo and I.Pak, Log-concavity of the partition function, (2013).S.Desalvo and I.Pak, Log-concavity of the partition function, (
Chen, W.Y.C., Wang, L.X.W., Xie, G.Y.B.: Finite differences of the logarithm of the partition function. Math. Comput. 85(298), 825–847 (2016) Article MathSciNet MATH Google Scholar DeSalvo, S., Pak, I.: Log-concavity of the partition function. Ramanujan J. 38, 61–73 ...
They noted that the log-concavity of {ℓn,kΛ}k=1n is equivalent to that of {in,kΛ}k=1n provided that the set Λ contains at most one partition with first row of length k for each 1≤k≤n. They further obtained the following results, see [2, Theorems 3.1, 3.2, 4.4 and 4.5...
本周我们的matroid theory讨论班正式开始上课,我们第一节课所讲述的主要内容是Dowling的一篇证明matroid的independent numbers在一定范围下的log-concavity的论文 [1]以及赵萃魁对一个加强的结论的证明[2],我在…
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 ...
Afterwards, the dihedral-angle and concavity of the surfaces is taken into account to produce the final segments. This kind of segmentation provides additional insights into the complexity of the parts that are forming the building element. Therefore, we count the segments, measure their area, and...
distributions, which need not arise as marginals of an asymp- totically mean stationary process (the most general condition under which such a theorem is known). Log-concavity is a global restriction on the joint distribution of the process, just like stationarity or ergodicity; however it is ...
of weakness, backbreak, concavity, unusual jointing and overhang. b) BLASTHOLE LAYOUT AND LOADING: Any deviation in the direction of a blast hole can reduce or increase theburden. While loading a hole, blasters must frequently check the rise of the explosives column...
log-concavitythe higher order Turán inequalitiesLetM0(n)(resp.M1(n)) denote the number of partitions ofnwith even (resp. odd) crank. Choi, Kang and Lovejoy established an asymptotic formula forM0(n)M1(n). By utilizing this formula with the explicit bound, we show thatMk(n1)+Mk(n+1...
The (strong) q-log-concavity of q-binomial coefficients has been extensively investigated. Recently, Dousse and Kim introduced an overpartition analogue of q-binomial coefficients, which is a generating function for the number of overpartitions fitting inside a rectangle. They also studied the (q...