相关论文: Dynamics of balanced parentheses, lexicographic se…

I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…

A new algorithm to generate all Dyck words is presented, which is used in ranking and unranking Dyck words. We emphasize the importance of using Dyck words in encoding objects related to Catalan numbers. As a consequence of formulas used in…

We study various aspects of Dyck words appearing in binary sequences, where $0$ is treated as a left parenthesis and $1$ as a right parenthesis. We show that binary words that are $7/3$-power-free have bounded nesting level, but this no…

We propose different ways of lifting the notion of Dyck language from words to 2-dimensional (2D) pictures, by means of new definitions of increasing comprehensiveness. Two of the proposals are based on alternative definitions of a Dyck…

We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves…

Dyck paths (also balanced brackets and Dyck words) are among the most heavily studied Catalan families. This paper is a continuation of [2, 3, 4]. In the paper we are dealing with the numbering of Dyck paths, with the resulting numbers, the…

We propose an original approach to the problem of rankunimodality for Dyck lattices. It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of…

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 with Dyck paths.

Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…

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…

A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic…

Many digital functions studied in the literature, e.g., the summatory function of the base-$k$ sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usually studied using techniques from analytic…

Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…

This paper investigates the dynamical properties of Dickson polynomials over finite fields, focusing on the periodicity and structural behavior of their iterated sequences. We introduce and analyze the sequence $[D_n(x, \alpha) \mod (x^q -…

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 considered in different coordinates. In the calculations, we…

The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…

This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…

We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to…

The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian…

The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…