2019/12/20 by Gennady Eremin, Eremin, Gennady
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.1912.09693
openalex publication_date 2019/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the core of mathematics is natural numbers. And everything related to the natural number is interesting to mathematicians. In this paper, we draw parallels between natural numbers and elements of a non-numeric lexicographic sequence, Motzkin words (well-formed strings of parentheses and zeros). We will also talk about the decomposition of Motzkin words into pairs of parentheses (analogue of Prime Numbers). Finally, we will try to interest the reader in the elements of mathematical analysis on bracket expressions. The nesting procedure of parentheses is described by the author as the differentiation of the weight function. We will work a little with derivatives for bracket pairs and also give some differential equations.