Combinatorics Problem Sets – Based on A Walk Through Combinatorics

This repository contains my organized solutions and study notes for Combinatorics, based primarily on the textbook A Walk Through Combinatorics by Miklós Bóna.

It serves as a personal study log and problem set archive as I work through core combinatorics concepts and example problems to deepen my problem-solving intuition and build a strong foundation for probability, statistics, and machine learning.

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Resource Used

All problems and theory are taken from:

Miklós Bóna, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory Link to book (Springer)

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Structure & Organization

Each folder corresponds to a major topic (loosely aligned with chapters in the book), and within it are subfiles for notes, quick_check, problems, and solutions.

combinatorics-problem-sets/
├── 00_prerequisite/
├── 01_basic_methods/
│   ├── 1a_pigeon_hole_principle
│   │   ├── problem_sets
│   │   ├── quick_check.ipynb
│   │   ├── README.md
│   ├── 1b_mathematical_induction
│   ├── ...
├── 02_enumerative_Combinatorics/
│   ├── ...
├── 03_graph_Theory/
│   ├── ...
├── 04_horizons/
└── README.md

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How I'm Solving

Most problems are:

• Solved by hand on paper first
• Then written up in Markdown files for long-term reference
• Accompanied by distilled notes on key ideas and strategies
• Sometimes simulated or visualized (when helpful)

The goal is not speed, but true mastery — as part of my Project10X foundational training in probability and statistics.

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Learning Objectives

• Build deep problem-solving fluency in combinatorics

• Apply combinatorial techniques confidently in probability, inference, and AI

• Gain mastery of foundational tools like:

  • Product and sum rules
  • Permutations and combinations
  • Binomial identities
  • Inclusion-Exclusion
  • Pigeonhole principle
  • Integer partitions and distributions
  • Recursion and generating functions
  • Intro to graph theory (optional chapters)

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Tools Used

• Markdown + Git for organized version control
• LaTeX for clean math typesetting
• Python (Jupyter) for simulating and verifying complex counts

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License

This repository is for educational and personal study use only. All original problems and content are copyright of Miklós Bóna.

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Created and Maintained by RM Villa.