拟半度量锥与平铺阶指数矩阵
The cone of quasi-semimetrics and exponent matrices of tiled orders
摘要：
$n$上的有限拟半度量可以被认为是完全有向图中满足所有可能的三角不等式的$n$顶点上的边的非负赋值。他们包括一个多面体锥的对称群进行了研究，小$n$的Deza，Dutour和Panteleeva。我们表明，对称性和组合对称群是因为他们所证明的。积分拟半度量在瓦序理论中有着特殊的地位，被称为指数矩阵，可以看作是分量极大值下的幺半群，我们给出了该幺半群的自同构群的一个新的推导.其中一些结果遵循更一般的考虑多面体锥，是封闭的分量最大。
英文摘要：
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.
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