论文标题
Chern-fu-tang猜想的多面式化
Polynomization of the Chern--Fu--Tang conjecture
论文作者
论文摘要
Bessenrodt和Ono在分区函数的添加和乘法性属性以及DeSalvo和Pak的纸上对分区函数的对数洞穴的纸张的工作产生了许多美丽的定理和猜想。 2020年1月，第一作者对波恩的MPIM进行了一次猜想的猜想，并提出了涉及多项式的扩展（与Neuhauser的联合工作）。部分结果已宣布。 Bringmann，Kane，Rolen和Tripp提供了Chern-fu--tang猜想的完整证明，遵循Ono的建议，以利用最近提供的分数分区功能提供的确切公式。他们还证明了海姆（Neuhauser）的猜想很大一部分，这是Chern-fu--tang的猜想的一级化。我们证明了几个案例，没有Bringmann等人涵盖。最后，我们提出了一种证明猜想的一般方法。
Bessenrodt and Ono's work on additive and multiplicative properties of the partition function and DeSalvo and Pak's paper on the log-concavity of the partition function have generated many beautiful theorems and conjectures. In January 2020, the first author gave a lecture at the MPIM in Bonn on a conjecture of Chern--Fu--Tang, and presented an extension (joint work with Neuhauser) involving polynomials. Partial results have been announced. Bringmann, Kane, Rolen and Tripp provided complete proof of the Chern--Fu--Tang conjecture, following advice from Ono to utilize a recently provided exact formula for the fractional partition functions. They also proved a large proportion of Heim--Neuhauser's conjecture, which is the polynomization of Chern--Fu--Tang's conjecture. We prove several cases, not covered by Bringmann et.\ al. Finally, we lay out a general approach for proving the conjecture.
