论文标题
$ q $ - 系的一致性涉及Baxter模型的Baxter解决方案的统计力学分区功能
$q$-Series congruences involving statistical mechanics partition functions in regime III and IV of Baxter's solution of the hard-hexagon model
论文作者
论文摘要
对于$ r_s（n）$的生成函数，对于每个$ s \ in \ {2,4 \} $，$ n $的分区数量为奇数零件，或一致于$ 0 $，$ \ pm s \ pm s \ pmod {10} $，在Rodney Baxter soldsitions of Hard-Hexagon Modelics的Rodney Baxter soluctime III中自然出现。 For each $s\in\{1,3\}$, the generating function of $R^*_s(n)$, the number of partitions of $n$ into parts not congruent to $0$, $\pm s\pmod {10}$ and $10-2s \pmod {20}$, arises naturally in regime IV of Rodney Baxter's solution of the hard-hexagon model of statistical力学。在本文中，我们调查了$ r_s（n）$和$ r^*_ s（n）$的均等，提供了新的奇偶校验结果，其中涉及分区编号$ p（n）$的总和和算术进度的正方形。
For each $s\in\{2,4\}$, the generating function of $R_s(n)$, the number of partitions of $n$ into odd parts or congruent to $0$, $\pm s\pmod {10}$, arises naturally in regime III of Rodney Baxter's solution of the hard-hexagon model of statistical mechanics. For each $s\in\{1,3\}$, the generating function of $R^*_s(n)$, the number of partitions of $n$ into parts not congruent to $0$, $\pm s\pmod {10}$ and $10-2s \pmod {20}$, arises naturally in regime IV of Rodney Baxter's solution of the hard-hexagon model of statistical mechanics. In this paper, we investigate the parity of $R_s(n)$ and $R^*_s(n)$, providing new parity results involving sums of partition numbers $p(n)$ and squares in arithmetic progressions.
