Combinatorics — Combinations and Binomial Theorem

Mathematics Geometry & Topology / Discrete Source: Standard discrete math texts Cite
Primary: Pascal, Newton
Publication: Binomial theorem
Year: 17th c.
URL: Wikipedia

Description

Combinations with repetition, binomial theorem, Pascal identity. 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") DefProd("DefProd Product principle") PermNoRep("PermNoRep Permutations no rep") CombNoRep("CombNoRep Combinations") CombRep("CombRep Combinations with rep") BinomThm("BinomThm Binomial theorem") Pascal("Pascal Pascal identity") DefFact --> PermNoRep DefProd --> PermNoRep PermNoRep --> CombNoRep DefFact --> CombNoRep CombNoRep --> CombRep CombNoRep --> BinomThm CombNoRep --> Pascal 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,DefProd definition class PermNoRep,CombNoRep,CombRep,BinomThm,Pascal theorem

Color Scheme

Red
Axioms
Blue
Definitions
Teal
Theorems

Statistics

  • Nodes: 7
  • Edges: 7

Keywords

  • combinatorics
  • permutations
  • combinations
  • binomial theorem
  • counting