论文标题
平面分区功能的Turán不平等
Turán inequalities for the plane partition function
论文作者
论文摘要
Heim，Neuhauser和Tröger最近为Macmahon的平面分区功能$ \ MATHRM {PL}（n）$建立了一些不平等现象，这些功能将已知结果概括为Euler的分区功能$ P（n）$。他们还推测$ \ mathrm {pl}（n）$是所有$ n \ geq 12的log-concave。$我们证明了这个猜想。此外，对于每$ d \ geq 1 $，我们都会证明他们的猜测$ \ mathrm {pl}（n）$满足了足够大的$ n $的学位$ d $turán的不平等。 $ d = 2 $的情况是log-concavity的情况。
Heim, Neuhauser, and Tröger recently established some inequalities for MacMahon's plane partition function $\mathrm{PL}(n)$ that generalize known results for Euler's partition function $p(n)$. They also conjectured that $\mathrm{PL}(n)$ is log-concave for all $n\geq 12.$ We prove this conjecture. Moreover, for every $d\geq 1$, we prove their speculation that $\mathrm{PL}(n)$ satisfies the degree $d$ Turán inequality for sufficiently large $n$. The case where $d=2$ is the case of log-concavity.
