4 citations · 12 across the 12 of their papers we have counts for
12 papers · 1 filter
Dyck Numbers, I. Successor Function
Gennady Eremin
Dyck paths are among the most heavily studied Catalan families. In the paper we are dealing with the minimal numbering of Dyck paths, with the resulting numbers, the terms of the O…
Walking in the OEIS: From Motzkin numbers to Fibonacci numbers. The "shadows" of Motzkin numbers
Gennady Eremin
In this paper, we consider nine OEIS sequences, the analysis of which allows us to find a connection between Motzkin numbers and Fibonacci numbers. In each Motzkin number, we disti…
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…