树的距离矩阵行列式与非相交路径
组合数学
2025-06-02 v2
摘要
我们提出了 Graham-Pollak 公式行列式关于树距离矩阵的首个组合论证明，借助反演配对和 Lindstr"om-Gessel-Viennot 引理。我们的方法提供了对现有 generalizations 和 型态的 Graham-Pollak 公式的统一理解框架，并促进了对其自然同时 generalizations 的推导。
引用
@article{arxiv.2407.01227,
title = {Non-intersecting paths and the determinant of the distance matrix of a tree},
author = {Emmanuel Briand and Luis Esquivias-Quintero and Álvaro Gutiérrez and Adrián Lillo and Mercedes Rosas},
journal= {arXiv preprint arXiv:2407.01227},
year = {2025}
}
备注
Changed the way in which networks are presented, in hopes of simplification and rigour. Technical details postponed to later sections. 37 pages, 15 figures