论文标题
跨分区和布雷索德的猜想，ii
Overpartitions and Bressoud's conjecture, II
论文作者
论文摘要
本文的主要目的是为Bressoud对Case $ J = 0 $的猜想提供答案，从而为猜想提供了完整的解决方案。 $ j = 1 $的案例最近已由金（Kim）解决。使用我们先前论文中普通分区函数$ b_0 $和过度分区功能$ \ Overline {B} _1 $之间建立的连接，我们发现Bressoud对Case $ J = 0 $的猜想的证明相当于确定对$ J = 1 $ $ j = 1 $的推测类似物的多项类似物。通过概括Kim的方法，我们以$ J = 1 $的猜想获得了所需的过度分区类似物，最终使我们能够确认Bressoud对Case $ J = 0 $的猜想。
The main objective of this paper is to present an answer to Bressoud's conjecture for the case $j=0$, resulting in a complete solution to the conjecture. The case for $j=1$ has been recently resolved by Kim. Using the connection established in our previous paper between the ordinary partition function $B_0$ and the overpartition function $\overline{B}_1$, we found that the proof of Bressoud's conjecture for the case $j=0$ is equivalent to establishing an overpartition analogue of the conjecture for $j=1$. By generalizing Kim's method, we obtain the desired overpartition analogue of Bressoud's conjecture for $j=1$, which eventually enables us to confirm Bressoud's conjecture for the case $j=0$.
