论文标题
希格曼猜想的箭袋类似物
A Quiver Analogue of Higman's Conjecture
论文作者
论文摘要
格雷厄姆·希格曼（Graham Higman）的一个未解决的猜想指出，$ n \ times n $ n $ unitriangular矩阵的共轭类别的数量在所有$ n \ geq 1 $中，在有限字段$ \ mathbb {f} _q $中是$ q $ polynomial in $ q $。在本文中，我们介绍了猜想的新箭量概括。在这种概括的推动下，我们证明了某些对Quivers的操作使相关的计数保持不变。基于这些不变性属性，我们解决了包含不超过两个长度的Quivers的引入的猜测，提供了明确的公式。
An unresolved conjecture by Graham Higman states that for all $n\geq 1$ the number of conjugacy classes of the group of $n \times n$ unitriangular matrices with entries in the finite field $\mathbb{F}_q$ is a polynomial in $q$. In this paper we introduce a new quiver generalization of the conjecture. Motivated by this generalization, we prove that certain operations on quivers leave the relevant counts unchanged. Based on these invariance properties, we solve the introduced conjecture for quivers containing no path of length exceeding two, providing explicit formulas.
