论文标题
Chern-Fu-Tang和Heim-Neuhauser的分数分区和猜想
Fractional partitions and conjectures of Chern-Fu-Tang and Heim-Neuhauser
论文作者
论文摘要
许多论文研究了分区功能的不平等现象。最近，在这种不平等现象中，许多论文考虑了加性和乘法行为之间的混合。特别是，Chern-Fu-Tang和Heim-Neuhauser就生成分区功能的功能系数提出了猜想。这些猜想是在彩色分区和Nekrasov-Okounkov公式的背景下提出的。在这里，我们研究了两个此类系数的产物差异的精确大小。这使我们能够证明Chern-Fu-Tang的猜想，并在一定范围内显示Heim-Neuhauser的猜想。所提供的明确错误术语也将在未来的分区不平等研究中有用。这些是针对对此类分析问题感兴趣的研究人员的用户友好方式进行的。
Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern-Fu-Tang and Heim-Neuhauser gave conjectures on inequalities for coefficients of powers of the generating partition function. These conjectures were posed in the context of colored partitions and the Nekrasov-Okounkov formula. Here, we study the precise size of differences of products of two such coefficients. This allows us to prove the Chern-Fu-Tang conjecture and to show the Heim-Neuhauser conjecture in a certain range. The explicit error terms provided will also be useful in the future study of partition inequalities. These are laid out in a user-friendly way for the researcher in combinatorics interested in such analytic questions.
