论文标题
分区及其应用的第二个转移差异
The second shifted difference of partitions and its applications
论文作者
论文摘要
许多最近的论文估计了分区功能$ p（n-j）/p（n）$的比率，这些比率出现在许多应用程序中。在这里，我们证明了这些比率易于使用的有效限制。然后，我们研究了分区的第二个转移差异，$ f（j，n）：= p（n）-2p（n-j） +p（n-2j）$，并给出$ f（j，n）$的另一个易于使用的估算。作为这些应用程序，我们证明了$ p（n）$的转移属性属性，并给出了$ k $ rank分区函数$ n_k（m，n）$和非$ k $ - $ y-ary分区的新估计。
A number of recent papers have estimated ratios of the partition function $p(n-j)/p(n)$, which appears in many applications. Here, we prove an easy-to-use effective bound on these ratios. Using this, we then study second shifted difference of partitions, $f(j,n):= p(n) -2p(n-j) +p(n-2j)$, and give another easy-to-use estimate of $f(j,n)$. As applications of these, we prove a shifted convexity property of $p(n)$, as well as giving new estimates of the $k$-rank partition function $N_k(m,n)$ and non-$k$-ary partitions along with their differences.
