论文标题
限制分区功能的对数concavity $ p_ \ mathcal {a}（n，k）$和新的bessenrodt-ono类型不等式
Log-concavity of the restricted partition function $p_\mathcal{A}(n,k)$ and the new Bessenrodt-Ono type inequality
论文作者
论文摘要
令$ \ mathcal {a} =（a_i）_ {i = 1}^\ infty $是一个非淘汰的正整数的序列，让$ k \ in \ mathbb {n} _+$修复。函数$ p_ \ mathcal {a}（n，k）$对$ n $的分区数量计数$ n $的分区数，而多零件中的零件$ \ {a_1，a_2，a_2，\ ldots，a_k \ \} $。我们发现了一种新型的bessenrodt-ono不等式，用于$ p_ \ mathcal {a}（n，k）$。此外，我们发现$ k $，$ \ {a_1，a_2，\ ldots，a_k \} $和$ n \ in \ mathbb {n} _+$，序列$ \ left（p_ \ \ mathcal {a}（n，k）\ right）我们的证明是基于$ p_ \ Mathcal {a}（n，k）$的渐近行为，尤其是我们应用了Netto和Pólya-Szegö的结果以及Almkavist的估计。
Let $\mathcal{A}=(a_i)_{i=1}^\infty$ be a non-decreasing sequence of positive integers and let $k\in\mathbb{N}_+$ be fixed. The function $p_\mathcal{A}(n,k)$ counts the number of partitions of $n$ with parts in the multiset $\{a_1,a_2,\ldots,a_k\}$. We find out a new type of Bessenrodt-Ono inequality for the function $p_\mathcal{A}(n,k)$. Further, we discover when and under what conditions on $k$, $\{a_1,a_2,\ldots,a_k\}$ and $N\in\mathbb{N}_+$, the sequence $\left(p_\mathcal{A}(n,k)\right)_{n=N}^\infty$ is log-concave. Our proofs are based on the asymptotic behavior of $p_\mathcal{A}(n,k)$, in particular, we apply the results of Netto and Pólya-Szegö as well as the Almkavist's estimation.
