论文标题
形成良好的括号字符串的算术。第二类的Motzkin数字
Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind
论文作者
论文摘要
在本文中，我们用零（motzkin单词）和相应的motzkin路径对形成良好的括号字符串进行算术化。所使用的转换让人联想到某种形式语言的数学对象的Gödel编号。我们构建了一个Motzkin系列，该系列与许多正式功能尽可能接近自然数量。括号字符串由三元代码和相应的自然数，第二种的Motzkin数字编码，这使得可以正式化和简化对后继函数的分析，以指定和阐明选择后续的过程。在符合良好的括号字符串的算术过程中，出现了各种特殊数字。在这方面，总而言之，我们将讨论一些$ 3^n+2 $的形式和镜像$ 2*3^n+1 $。
In this paper, we perform an arithmetization of well-formed parenthesis strings with zeros (Motzkin words) and of corresponding Motzkin paths. The transformations used are reminiscent of Gödel numbering for mathematical objects of some formal language. We construct a Motzkin series that is as close as possible to natural numbers by many formal features. Parenthesis strings are encoded by ternary codes and corresponding natural numbers, Motzkin numbers of the 2nd kind, which made it possible to formalize and simplify the analysis of the successor function, to specify and clarify the procedure for selecting a successor. In the process of arithmetization of well-wormed parenthesis strings, various special numbers appeared. In this regard, in conclusion we will talk a little about numbers of the form $3^n+2$ and mirror numbers $2*3^n+1$.
