Dyck Paths in Four-Dimensional Space

TL;DR

This paper explores the properties of Dyck paths within four-dimensional space, focusing on the construction of a Dyck triangle in an integer lattice to analyze balanced parentheses.

Contribution

It introduces a novel four-dimensional framework for Dyck paths and constructs the Dyck triangle in a four-dimensional integer lattice.

Findings

Defined the four-dimensional Dyck paths

Constructed the Dyck triangle in 4D lattice

Provided insights into balanced parentheses analysis

Abstract

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.