论文标题
瓷砖订单的准隔离和指数矩阵的锥
The cone of quasi-semimetrics and exponent matrices of tiled orders
论文作者
论文摘要
$ n $上的有限准半径可以将其视为$ n $顶点的完整有向图的边缘上的无负估值，这满足了所有可能的三角形不平等。他们组成了一个多面体锥体，其对称群是由Deza，Dutour和Panteleeva研究的小$ N $。我们表明，对称和组合对称组是猜想的。积分准半学分在瓷砖阶的理论中具有敏锐的位置，称为指数矩阵，并且可以在最大程度上将其视为单型矩阵；我们提供了该单体自动形态群体的新型推导。其中一些结果来自更一般地考虑在最大值下封闭的多面体锥。
Finite quasi semimetrics on $n$ can be thought of as nonnegative valuations on the edges of a complete directed graph on $n$ vertices satisfying all possible triangle inequalities. They comprise a polyhedral cone whose symmetry groups were studied for small $n$ by Deza, Dutour and Panteleeva. We show that the symmetry and combinatorial symmetry groups are as they conjectured. Integral quasi semimetrics have apecial place in the theory of tiled orders, being known as exponent matrices, and can be viewed as monoids under componentwise maximum; we provide a novel derivation of the automorphism group of that monoid. Some of these results follow from more general consideration of polyhedral cones that are closed under componentwise maximum.
