渐近性，Turán不等式，以及BG-秩和2-商秩的分布
Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions
摘要：
令$j,n$是偶正整数，并且令$\overline{p}_j(n)$表示具有BG秩$j$的分区的数量，并且令$\overline{p}_j(a,b;n)$是具有BG秩$j$和$2$ -商秩与$a \pmod{b}$全等的分区的数量。我们给这两个统计量的渐近性，并表明，$\overline{p}_j(a,b;n)$是渐近等分布的同余类模$b$。我们还证明了$\overline{p}_j(n)$和$\overline{p}_j(a,b;n)$都渐近满足所有高阶Turán不等式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
