论文标题
渐近学，Turán不平等以及BG级分配和2 Quortient Cartitions的分布
Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions
论文作者
论文摘要
让$ j，n $甚至是积极的整数，然后让$ \ overline {p} _j（n）$表示带有bg rank $ j $的分区数，以及$ \ overline {p} _j（a，b; n）$，是BG-rank $ j $ j $ j $和$ 2 $ $ 2 $ quort $ quort $ quort $ $ quort $ p p p p p p p ps a a的分区数。我们给出了两个统计信息的渐近学，并表明$ \ overline {p} _j（a，b; n）$在同等类别modulo $ b $上渐近地分布。我们还表明，$ \ Overline {p} _j（n）$和$ \ overline {p} _j（a，b; n）$渐近地满足所有高阶Turán的所有不平等。
Let $j,n$ be even positive integers, and let $\overline{p}_j(n)$ denote the number of partitions with BG-rank $j$, and $\overline{p}_j(a,b;n)$ to be the number of partitions with BG-rank $j$ and $2$-quotient rank congruent to $a \pmod{b}$. We give asymptotics for both statistics, and show that $\overline{p}_j(a,b;n)$ is asymptotically equidistributed over the congruence classes modulo $b$. We also show that each of $\overline{p}_j(n)$ and $\overline{p}_j(a,b;n)$ asymptotically satisfy all higher-order Turán inequalities.
