Bhargava贪心胚作为高斯消元贪心胚
组合数学
2024-05-30 v5 离散数学
摘要
受Manjul Bhargava的广义阶乘理论启发，Fedor Petrov和作者定义了“Bhargava贪心胚”——一个分配给任意“超三元组”（有限超度量空间的一种扩展变体）的贪心胚（有限集上的类似拟阵的集合系统）。这里我们证明，有限超三元组的Bhargava贪心胚总是任意足够大（例如无限）域上的“高斯消元贪心胚”；这是可表示拟阵的贪心胚类比。我们找到了确保这一点的域大小的必要和充分条件。
引用
@article{arxiv.2001.05535,
title = {The Bhargava greedoid as a Gaussian elimination greedoid},
author = {Darij Grinberg},
journal= {arXiv preprint arXiv:2001.05535},
year = {2024}
}
备注
71 pages. Pages 1-39 are the core; the rest proves the optimality of the bound (under certain conditions) and fills in some very basic details. See http://www.cip.ifi.lmu.de/~grinberg/algebra/fps20gfv.pdf for a streamlined survey. Comments are welcome! v5 corrects a few typos and adds Example 2.5. This is NOT the published version!