Bessenrodt-Ono不等式的归纳证明
Proof of the Bessenrodt--Ono inequality by Induction
摘要：
2016年，Bessenrodt-Ono发现了一个不等式，解决了分拆函数的加法和乘法性质。推广由几个作者已经给出;分区与秩在一个给定的剩余类侯-Jagadeesan和男性，对$k$ -经常分区贝克-Bessenrodt，对$k$ -有色分区陈省身，傅，唐，海姆-Neuhauser对他们的多项式，和Dawsey-马斯里的安德鲁斯${\it spt}$ -功能。证明依赖于非平凡的渐近公式有关的圆方法的一面，或一个复杂的组合证明发明的Alanazi-Gagola-Munagi。本文给出了Bessenrodt-Ono不等式的一个新的证明，它建立在一个著名的关于划分数的递推公式上.我们将证明推广到Chern-Fu-Tang的结果及其多项式化。最后，我们还得到了一个新的结果。
英文摘要：
In 2016 Bessenrodt--Ono discovered an inequality addressing additive and multiplicative properties of the partition function. Generalization by several authors have been given; on partitions with rank in a given residue class by Hou--Jagadeesan and Males, on $k$-regular partitions by Beckwith--Bessenrodt, on $k$-colored partitions by Chern, Fu, Tang, and Heim--Neuhauser on their polynomization, and Dawsey--Masri on the Andrews ${\it spt}$-function. The proofs depend on non-trivial asymptotic formulas related to the circle method on one side, or a sophisticated combinatorial proof invented by Alanazi--Gagola--Munagi. We offer in this paper a new proof of the Bessenrodt--Ono inequality, which is built on a well-known recursion formula for partition numbers. We extend the proof to the result of Chern--Fu--Tang and its polynomization. Finally, we also obtain a new result.
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