2019/11/05 by Gennady Eremin, Eremin, Gennady · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1911.01673
17 pages
arxiv created 2019/11/05 · openalex publication_date 2019/11/05 · arxiv updated 2019/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a total lexicographical order on the set of Motzkin words. Elements are ordered similarly to Natural Numbers in accordance with known rules (axioms). As a result, we were able to obtain arithmetic and logical operations on the elements of the ordered sequence, Motzkin Row. This sequence consists of balanced brackets without leading zeros, with the exception of the initial word "0". It is the word "0" as well as the alphabetical symbol "0" that are analogues of numeric zero in the corresponding operations. Logical operations allow you to navigate Motzkin Row. Operations on words are accompanied by index equations, index polynomials.