4 citations · 12 across the 13 of their papers we have counts for
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Mathematics of Balanced Parentheses: The case of Ordered Motzkin Words
Gennady Eremin
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…
Arithmetic on Balanced Parentheses: The case of Ordered Motzkin Words
Gennady Eremin
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 w…
Dynamics of balanced parentheses, lexicographic series and Dyck polynomials
Gennady Eremin
The article deals with a lexicographic order in various sequences. Consider the axiomatic of lexicographic series, based on the properties of the natural numbers. Elements of the s…
Factoring Catalan numbers
Gennady Eremin
The paper describes a prime factorization of the Catalan numbers. Odd prime factors are distributed in layers in accordance with Legendre's formula. The content of each layer is a…
Legendre's formula and -adic analysis
Gennady Eremin
In number theory, we know Legendre's formula , which calculates the -adic valuation of the factorial, i.e. the exponent…
Dyck Paths in Four-Dimensional Space
Gennady Eremin
In analyzing balanced parentheses, we consider a group of related variables in Dyck paths. In the four-dimensional space, the Dyck triangle is constructed, i.e. an integer lattice…