论文标题
三角形和unitriangular矩阵的分支规则和通勤概率
Branching rules and commuting probabilities for Triangular and Unitriangular matrices
论文作者
论文摘要
本文涉及$ k $ tuplass $ k $ tuplass $ gt_n $ gt_n（\ mathbf f_q）$和unitriangular $ ut_m（\ mathbf f_q）$的同时列举矩阵的列举。通过计算分支规则，以$ n = 2,3,4 $和$ m = 3,4,5 $进行完成。此外，使用如此计算的分支矩阵，我们明确地在每种情况下明确获取$ k \ leq 5 $的通勤概率$ cp_k $。
This paper concerns the enumeration of simultaneous conjugacy classes of $k$-tuples of commuting matrices in the upper triangular group $GT_n(\mathbf F_q)$ and unitriangular group $UT_m(\mathbf F_q)$ over the finite field $\mathbf F_q$ of odd characteristic. This is done for $n=2,3,4$ and $m=3,4,5$, by computing the branching rules. Further, using the branching matrix thus computed, we explicitly get the commuting probabilities $cp_k$ for $k\leq 5$ in each case.
