论文标题
一类线性订单的欧几里得算法
Euclidean algorithm for a class of linear orders
论文作者
论文摘要
借用Marcone和Montálban在签名的树类和不可分解的散射线性订单的等法类别之间的一对一对应关系中借用灵感，我们发现签名的树的子类具有与不可分解的有限有限的有限级排名离散线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性相似的对应。 我们还介绍了\ emph {有限呈现的线性订单}的类 - 包含$ \ mathbf 1 $，$ω$和$ω^*$的有限等级线性订单的最小子类，并按照有限的总和和词典产物关闭。对于此类，我们开发了欧几里得算法的概括，其中线性顺序的\ emph {width}起着欧几里得规范的作用。使用此工具，我们使用\ emph {3签名的树}根据其演示文稿的等价关系对有限呈现的线性顺序的同构类别进行分类。
Borrowing inspiration from Marcone and Montálban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an analogous correspondence with equimorphism classes of indecomposable finite rank discrete linear orders. We also introduce the class of \emph{finitely presented linear orders}-- the smallest subclass of finite rank linear orders containing $\mathbf 1$, $ω$ and $ω^*$ and closed under finite sums and lexicographic products. For this class we develop a generalization of the Euclidean algorithm where the \emph{width} of a linear order plays the role of the Euclidean norm. Using this as a tool we classify the isomorphism classes of finitely presented linear orders in terms of an equivalence relation on their presentations using \emph{3-signed trees}.
