Combinatorics

Bridge Deep

Combinatorics is the counting layer of the repo. It is where "how many?" stops being ad hoc and becomes structured.

Use This Area When

• the real question is counting valid arrangements rather than finding one witness
• choices are constrained by runs, bounds, or symmetry
• direct brute force is blocked, but the structure of the objects is regular

Start With One Route

If your bottleneck is...	Open first	Then
basic counting patterns	Counting Basics	Bounded Compositions
overcounting and cancellation	Inclusion-Exclusion	one subset-style counting anchor
symmetry and orbit counting	Burnside / Pólya / Group Actions	compare against plain counting first
ranking and constructive counting	Lexicographic Enumeration	one ranking/unranking flavored note

Core Progression

1. Core first
2. Counting Basics

3. Bounded Compositions

4. Then add

5. Inclusion-Exclusion

6. Lexicographic Enumeration

7. Later

8. Burnside / Pólya / Group Actions
9. generating functions and deeper transform-heavy counting outside the current core

Good First Repo Anchors

• Distributing Apples
• Prime Multiples
• Counting Necklaces
• VOSFENCE
• VOITSORT

Browse All Subtopics

• Counting Basics
• Burnside / Pólya / Group Actions
• Inclusion-Exclusion
• Bounded Compositions
• Lexicographic Enumeration

Go Deeper

• Reference: CP-Algorithms
• Reference: OI Wiki
• Practice: CSES Problem Set