论文标题
一种研究与多编码相关的子迁移的组合方法
A combinatorial approach to study subshifts associated with multigraphs
论文作者
论文摘要
有限的许多符号可以描述为有限类型的subfrifts shift，可以描述为在挖掘上的所有无限步行的集合，最多从顶点到另一个边缘到另一个边缘。相关的有限设置禁止单词的$ \ f $是一个约束，它完全决定了转移的语言。在本文中，为了描述在多编码上的无限步行，我们介绍了单词（有限步行）的多样性概念，并将重复的单词定义为具有至少$ 2 $的多种单词。通常，对于给定的收集$ \ f $，禁止单词的$ \ f $带有预分配的多重性的重复单词的$ \ r $，我们定义了一种通用语言的概念，该语言是多版本。我们获得了与$ \ f $和$ \ r $相关的子班，以便使用广义语言计算其熵。我们还研究了该次移语言与广义语言之间的关系。然后，我们获得了生成函数的组合表达式，该函数列举了这种广义语言中固定长度的单词数量。这给出了邻接矩阵的perron根和特征向量，并具有与基础多编码相关的整数条目。使用此情况，获得了相关边缘移位的拓扑熵和帕里度量的替代定义。我们还讨论了Markov措施在此子移位上的某些特性。
A subshift of finite type over finitely many symbols can be described as a collection of all infinite walks on a digraph with at most a single edge from a vertex to another. The associated finite set $\F$ of forbidden words is a constraint which determines the language of the shift entirely. In this paper, in order to describe infinite walks on a multigraph, we introduce the notion of multiplicity of a word (finite walk) and define repeated words as those having multiplicity at least $2$. In general, for given collections $\F$ of forbidden words and $\R$ of repeated words with pre-assigned multiplicities, we define notion of a generalized language which is a multiset. We obtain a subshift associated with $\F$ and $\R$ such that its entropy is calculated using the generalized language. We also study the relationship between the language of this subshift and the generalized language. We then obtain a combinatorial expression for the generating function that enumerates the number of words of fixed length in this generalized language. This gives the Perron root and eigenvectors of the adjacency matrix with integer entries associated to the underlying multigraph. Using this, the topological entropy and an alternate definition of Parry measure for the associated edge shift are obtained. We also discuss some properties of Markov measures on this subshift.
