4 citations · 12 across the 15 of their papers we have counts for
6 papers · 1 filter
Arithmetization of well-formed parenthesis strings. Motzkin Numbers of the Second Kind
Gennady Eremin
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 reminisc…
4D Dyck triangle and its projections
Gennady Eremin
The classic Dyck triangle, the Catalan triangle, and the Catalan convolution matrix are plane projections of the multidimensional Dyck triangle. In the Dyck path, each node is uniq…
Decomposition of the Catalan number into the sum of squares
Gennady Eremin
Analysis of the dynamics of the Dyck words helped solve the problem of representing the Catalan number as a sum of squares of natural numbers. In this case, the Dyck triangle is co…
Naturalized bracket row and Motzkin triangle
Gennady Eremin
The paper considers the sequence of the Motzkin words, which is constructed according to formal features of natural numbers. We investigate the decomposition of well-formed parenth…
Factoring Middle Binomial Coefficients
Gennady Eremin
The article describes prime intervals into the prime factorization of the middle binomial coefficient. Prime factors and prime powers are distributed in layers. Each layer consists…
Generating function for Naturalized Series: The case of Ordered Motzkin Words
Gennady Eremin
We continue to consider the ordered lexicographic sequence, which is constructed according to the formal characteristics of a series of natural numbers. For analysis, we selected b…