Fibonacci and Catalan Lattice Paths 🔢

This project examines the combinatorial properties of wall-constrained lattice paths, focusing on their connections to classical sequences such as Fibonacci, Catalan, and Motzkin numbers.

📝 About The Project

This study utilizes the following to analyze the combinatorial properties of lattice paths:

• Path generation algorithms
• Transformation techniques
• Visualization tools

This project is accompanied by an academic paper that provides detailed mathematical analysis and theoretical background. You can find the paper in the docs/paper directory.

🛠️ Built With

• Python
• Matplotlib
• NumPy
• NetworkX

📁 Project Structure

Fibonacci-Catalan-Lattice-Paths/
├── src/                    # Source code files
│   ├── paths/             # Path generation and transformation
│   ├── visualization/     # Visualization tools
│   └── utils/            # Utility functions
├── tests/                 # Test files
├── docs/                  # Documentation
│   └── paper/            # Academic paper and related materials
├── examples/              # Example notebooks and scripts
├── data/                  # Data files
├── requirements.txt       # Project dependencies
└── README.md             # Project documentation

🚀 Getting Started

Prerequisites

pip install -r requirements.txt

Installation

git clone https://github.com/burakyalcin10/DMPROJECT
cd DMPROJECT

📊 Features

• Fibonacci path generation and visualization
• Wall tiling structures
• Dyck path transformations
• Motzkin path transformations
• 3D lattice paths
• Parallelogram grid structures

📖 Academic Paper

The theoretical foundation and detailed analysis of this project are presented in our academic paper:

Title: Fibonacci and Catalan Paths: A Combinatorial Study in Lattice Walls
Authors: Elif Buse Cinar, Musa Talat Demir, Burak Yalcin, Mustafa Guvez, Yahya Efe Kurucay, Hüseyin Bardakci
Institution: Department of Computer Science, Akdeniz University, Antalya, Turkey

The complete paper can be found in the docs/paper directory.

👥 Contributors

• Elif Buse Cinar - Conceptualization, Original Draft
• Musa Talat Demir - Data Curation, Software, Validation
• Burak Yalcin - Methodology, Investigation, Formal Analysis, Programming
• Mustafa Guvez - Resources, Project Administration, Supervision
• Yahya Efe Kurucay - Review & Editing, Visualization
• Huseyin Bardakci - Validation, Resources

📚 References

For detailed references, please refer to the bibliography section of the paper.