论文标题
Bhargava贪婪作为高斯消除贪婪
The Bhargava greedoid as a Gaussian elimination greedoid
论文作者
论文摘要
Fedor Petrov和作者受到Manjul Bhargava的广义阶乘理论的启发，定义了“ Bhargava Greedoid” - 分配给任何“ Ultra Triple”的贪婪（一种有限套件的纯种套件）（在有限三重的有限套件上）（有限的有限型超级图的变体）。在这里，我们表明，有限的Ultra Triple的Bhargava贪婪始终是任何足够大的（例如，无限）场上的“高斯消除贪婪”。这是代表性矩阵的贪婪类似物。我们发现田间大小的必要条件以确保这一点。
Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Petrov and the author have defined the "Bhargava greedoid" -- a greedoid (a matroid-like set system on a finite set) assigned to any "ultra triple" (a somewhat extended variant of a finite ultrametric space). Here we show that the Bhargava greedoid of a finite ultra triple is always a "Gaussian elimination greedoid" over any sufficiently large (e.g., infinite) field; this is a greedoid analogue of a representable matroid. We find necessary and sufficient conditions on the size of the field to ensure this.
