论文标题
分配格的总排序不变地图
Total orderization invariant maps on distributive lattices
论文作者
论文摘要
考虑到任何有限的子集$ a $ a $ n $的分布式晶格和$ k \ in \ {1，...，...，n \} $，中间操作的自然扩展为$ n $变量，这概述了$ k $ th $ a $的最小元素的概念。通过将这些操作中的每一个应用于$ A $，可以获得完全订购的设置$（a）$。我们将$提及（a）$是$ a $的总订购。在对分布晶格上制定了总排序不变图的简要理论之后，本文显示了这些功能如何推广并为对称连续的正相均匀函数，有限的正常对称性多线性图和对载体晶格上的某些功率总和的新特征提供了新的特征。这些定理概括了Bernau，Huijsmans，Kusraev，Azouzi，Boulabiar，Bulabiar，Buskes，Boyd，Ryan和Snigireva，然后又揭示了本文研究的各种地图的新颖性能。
Given any finite subset $A$ of order $n$ of a distributive lattice and $k\in\{1,...,n\}$, there is a natural extension of the median operation to $n$ variables which generalizes the notion of the $k$th smallest element of $A$. By applying each of these operations to $A$, a totally ordered set $to(A)$ is obtained. We refer to $to(A)$ as the total orderization of $A$. After developing a brief theory of total orderization invariant maps on distributive lattices, it is shown in this paper how these functions generalize and provide new characterizations for symmetric continuous positively homogeneous functions, bounded orthosymmetric multilinear maps, and certain power sum polynomials on vector lattices. These theorems generalize several results by Bernau, Huijsmans, Kusraev, Azouzi, Boulabiar, Buskes, Boyd, Ryan, and Snigireva and in turn reveal novel properties of the various maps studied in this paper.
