Description
Pigeonhole principle, inclusion-exclusion, derangements, Stirling numbers. Shows how counting formulas depend on principles and prior results.
Source: Discrete Mathematics: An Open Introduction; standard combinatorics texts
Dependency Flowchart
Note: Arrows mean "depends on" (tail to head).
graph TD
DefFact("DefFact Factorial")
DefSum("DefSum Sum principle")
DefProd("DefProd Product principle")
PermNoRep("PermNoRep Permutations no rep")
Pigeonhole("Pigeonhole Pigeonhole principle")
InclExcl("InclExcl Inclusion-exclusion")
InclExcl3("InclExcl3 Incl-excl 3 sets")
Derange("Derange Derangements")
Stirling2("Stirling2 Stirling numbers")
DefFact --> PermNoRep
DefProd --> PermNoRep
DefSum --> Pigeonhole
DefSum --> InclExcl
InclExcl --> InclExcl3
InclExcl --> Derange
PermNoRep --> Derange
DefSum --> Stirling2
DefProd --> Stirling2
classDef axiom fill:#ff6b6b,color:#fff,stroke:#c0392b
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class DefFact,DefSum,DefProd definition
class PermNoRep,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem
Color Scheme
Red
Axioms
Axioms
Blue
Definitions
Definitions
Teal
Theorems
Theorems
Statistics
- Nodes: 9
- Edges: 9
Keywords
- combinatorics
- permutations
- combinations
- binomial theorem
- counting